de Sitter Vacua in the String Landscape
The late-time behavior of our universe is one of accelerated expansion, or that of a de Sitter space, and therefore motivates us to look for time-dependent backgrounds. Finding such backgrounds in string theory has always been a challenging problem. An even harder problem is to find time-dependent backgrounds that allow positive dark energies. As a first step to handle such scenarios, we study a time-dependent background in type IIB theory, with four-dimensional de Sitter isometries, by uplifting it to M-theory and then realizing it as a coherent, or squeezed-coherent, state over an appropriate solitonic configuration. While classically such a background does not solve the equations of motion, the corresponding Schwinger-Dyson equations reveal that there are deeper issues that may even prohibit a solution to exist at the quantum level, as long as the internal space remains time-independent. A more generic analysis is then called for, where both the effective four-dimensional space-time, the internal space, and the background fluxes are all time-dependent. We study in details such a background by including perturbative and non-perturbative as well as local and non-local quantum terms. Our analysis reveals a distinct possibility of the emergence of a four-dimensional positive curvature space-time with de Sitter isometries and time-independent Newton's constant in the landscape of type IIB string theory. We argue how the no-go and the swampland criteria are avoided in generating such a background, and compare it with other possibilities involving backgrounds with time-dependent Newton constants. These time-varying Newton constant backgrounds typically lead to unavoidable late time singularities, amongst other issues.

Lectures on the Swampland Program in String Compactifications
The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland conjectures. In these lecture notes, we provide a pedagogical introduction to the most important Swampland conjectures, their connections and their realization in string theory compactifications. The notes are based on the series of lectures given by Irene Valenzuela at the online QFT and Geometry summer school in July 2020.

String Geometry and Non-perturbative Formulation of String Theory
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert action coupled with gauge fields, and formulate superstring theory non-perturbatively by summing over metrics and the gauge fields on the spaces of strings. This theory does not depend on backgrounds. The theory has a supersymmetry as a part of the diffeomorphisms symmetry on the superstring manifolds. We derive the all-order perturbative scattering amplitudes that possess the super moduli in type IIA, type IIB and SO(32) type I superstring theories from the single theory, by considering fluctuations around fixed backgrounds representing type IIA, type IIB and SO(32) type I perturbative vacua, respectively. The theory predicts that we can see a string if we microscopically observe not only a particle but also a point in the space-time. That is, this theory unifies particles and the space-time.

KKLT and the Swampland Conjectures
Recently, various swampland conjectures have been proposed that every UV complete effective field theory should satisfy. In particular, these deal with the properties of AdS and dS solutions arising in theories of quantum gravity. Mainly summarizing the results of our two previous articles [here and here], we confront the string theory based KKLT scenario with these conjectures and argue that if quantum vacua as in the KKLT construction indeed exist, some of the conjectures receive some log-corrections. Furthermore we point out some new aspects not contained in the aforementioned two papers.

Geometric Unification of Higgs Bundle Vacua
Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of branes give rise to different low energy effective field theories. This has been heavily used in the study of M-theory on local G2 spaces and F-theory on local elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D N = 1 effective field theory defined by M-theory on a local Spin(7) space unifies the Higgs bundle data associated with 4D N = 1 M- and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory on such local Spin(7) spaces, and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing Spin(7) spaces from generalized connected sums.

String landscape and fermion masses
Besides the string scale, string theory has no parameter except some quantized flux values, and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution PðQÞ of a physical quantity Q (with nonnegative dimension) tends to peak (diverge) at Q ¼ 0 as a signature of string theory. In the Racetrack Kähler uplift model, where PðΛÞ of the cosmological constant Λ peaks sharply at Λ ¼ 0, the electroweak scale (not the electroweak model) naturally emerges when the median Λ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution PðmÞ that diverges at m ¼ 0, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be Pmν ≃ 0.0592 eV, with an upper bound Pmν < 0.066 eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-N limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.

de Sitter minima from M-theory and string theory
We study M-theory compactification on T7=Z3 2 in the presence of a seven-flux, metric fluxes, and KK monopoles. The effective four-dimensional supergravity has seven chiral multiplets whose couplings are specified by the G2-structure of the internal manifold. We supplement the corresponding superpotential by a KKLT type nonperturbative exponential contribution for all, or for some of the seven moduli, and find a discrete set of supersymmetric Minkowski minima. We also study type IIA and type IIB string theory compactified on T6=Z22. In type IIA, we use a six-flux, geometric fluxes, and nonperturbative exponents. In type IIB theory, we use F and H fluxes, and nongeometric Q and P fluxes, corresponding to consistently gauged supergravity with certain embedding tensor components, without nonperturbative exponents. Also in these situations, we produce discrete Minkowski minima. Finally, to construct dS vacua starting from these Minkowski progenitors, we follow the procedure of mass production of dS vacua.

Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce catastrophic instabilities and classic solutions become unstable under small perturbations or their evolutions. In this paper we discuss theoretical validity of the semiclassical gravity from the perspective of the spacetime instabilities and consider cosmological dynamics of the Universe in this theory. We clearly show that the homogenous and isotropic flat Universe is unstable and the solutions either grow exponentially or oscillate even in Planckian time tI = (α1GN ) 1/2 ≈ α110−43 sec. The subsequent curvature evolution leads to Planck-scale spacetime curvature in a short time and causes a catastrophe of the Universe unless one takes extremely large values of the gravitational couplings. Furthermore, we confirm the above suggestion by comparing the semiclassical solutions and ΛCDM with the Planck data and it is found that the semiclassical solutions are not consistent with the cosmological observations. Thus, the standard semiclassical gravity using quantum energy momentum tensor <Tµν> is not appropriate to describe our Universe.

Holography for the very early universe and the classic puzzles of hot big bang cosmology

**Abstract:**We show that standard puzzles of hot big bang cosmology that motivated the introduction of cosmological inflation, such as the smoothness and horizon problem, the flatness problem, and the relic problem are also solved by holographic models for very early universe based on perturbative three dimensional QFT. In the holographic setup, cosmic evolution is mapped to inverse renormalization group (RG) flow of the dual QFT, and the resolution of the puzzles relies on properties of the RG flow.**Conclusion**: In this paper we have shown that the (nongeometric) holographic cosmology model of [33] is capable of solving the standard problems of hot big bang cosmology: the smoothness and horizon problems, the flatness problem and the monopole and relic problems. In holographic cosmology time evolution translates into inverse RG flow and these problems are naturally resolved using properties of the RG flow. In these models the resolution of the initial singularity is mapped to the IR finiteness of the dual QFT and the arrow of time is linked with the monotonicity of RG flow. Together with the previously found fact that the CMBR fitting is as good as for standard ΛCDM with inflation our results mean that holographic cosmology is a viable alternative for a Standard Model of cosmology.Four Dimensional N=4 SYM and the Swampland
We consider supergravity theories with 16 supercharges in Minkowski space with dimensions d > 3. We argue that there is an upper bound on the number of massless modes in such theories depending on d. In particular we show that the rank of the gauge symmetry group G in d dimensions is bounded by rG ≤ 26 − d. This in particular demonstrates that 4 dimensional N = 4 SYM theories with rank bigger than 22, despite being consistent and indeed finite before coupling to gravity, cannot be consistently coupled to N = 4 supergravity in Minkowski space and belong to the swampland. Our argument is based on the swampland conditions of completeness of spectrum of defects as well as a strong form of the distance conjecture and relies on unitarity as well as supersymmetry of the worldsheet theory of BPS strings. The results are compatible with known string constructions and provide further evidence for the string lamppost principle (SLP): that string theory lamppost seems to capture all consistent quantum gravitational theories.

Amplitudes, resonances, and the ultraviolet completion of gravity
This paper constructs, making use of the on-shell spinor-helicity formalism, a possible ultraviolet completion of gravity following a “bottom-up” approach. The assumptions of locality, unitarity, and causality i) require an infinite tower of resonances with increasing spin and quantized mass, ii) introduce a duality relation among crossed scattering channels, and iii) dress all gravitational amplitudes in the Standard Model with a form factor that closely resembles either the Veneziano or the Virasoro-Shapiro amplitude in string theory. As a consequence of unitarity, the theory

*predicts*leading order deviations from General Relativity in the coupling of gravity to fermions that could be explained if space-time has torsion in addition to curvature. The ambitious and overarching question lurking in the background is uniqueness: are fundamental principles like unitarity and locality so demanding as to select one theory of gravity only? We believe that the bottom-up approach may help in shedding light on this question, see Ref. [22] for a related discussion. In this regard, our findings have glaring similarities with string theory, tantalizingly yet inconclusively in line with the belief that string theory is the only consistent quantum theory of gravity.F-theory at order α′3
We study the effective physics of F-theory at order α′ 3 in derivative expansion. We show
that the ten-dimensional type IIB eight-derivative couplings involving the graviton and the axio-dilaton naturally descend from pure gravity in twelve dimensions. Upon compactification on elliptically fibered Calabi-Yau fourfolds, the non-trivial vacuum profile for the axio-dilaton leads to a new, genuinely N = 1, α′ 3 correction to the four-dimensional effective action.

Emergent Strings from Infinite Distance Limits
As a refinement of the Swampland Distance Conjecture, we propose that a quantum
gravitational theory in an infinite distance limit of its moduli space either decompactifies,
or reduces to an asymptotically tensionless, weakly coupled string theory. We support
our claim by classifying, as special cases, the behaviour of M-Theory and Type IIA string
theory compactifications on Calabi-Yau three-folds at infinite distances in Kahler moduli
space. The analysis comprises three parts: We first classify the possible infinite distance
limits in the classical Kahler moduli space of a Calabi-Yau three-fold. Each such limit
at finite volume is characterized by a universal fibration structure, for which the generic
fiber shrinking in the limit is either an elliptic curve, a K3 surface, or an Abelian surface.
In the second part we focus on M-Theory and investigate the nature of the towers of
asymptotically massless states that arise from branes wrapped on the shrinking fibers.
Depending on which of the three classes of fibrations are considered, we obtain decompactification to F-Theory, or a theory with a unique asymptotically tensionless, weakly coupled heterotic or Type II string, respectively. The latter probes a dual D-manifold which is in general non-geometric. In addition to the intrinsic string excitations, towers of states from M2-branes along non-contractible curves become light and correspond to further wrapping and winding modes of the tensionless heterotic or Type II string. In the third part of the analysis, we consider Type IIA string theory on Calabi-Yau three-folds and show that quantum effects obstruct taking finite volume infinite distance limits in the Kahler moduli space. The only possible infinite distance limit which is not a decompactification limit involves K3-fibrations with string scale fiber volume and gives
rise to an emergent tensionless heterotic string.

Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory
We study string loop corrections to the gravity kinetic terms in type IIB compactifications
on Calabi-Yau threefolds or their orbifold limits, in the presence of D7-branes and orientifold
planes. We show that they exhibit in general a logarithmic behaviour in the large volume
limit transverse to the D7-branes, induced by a localised four-dimensional Einstein-Hilbert
action that appears at a lower order in the closed string sector, found in the past. Here, we
compute the coefficient of the logarithmic corrections and use them to provide an explicit
realisation of a mechanism for K¨ahler moduli stabilisation that we have proposed recently,
which does not rely on non-perturbative effects and lead to de Sitter vacua. Our result avoids
no-go theorems of perturbative stabilisation due to runaway potentials, in a way similar to
the Coleman-Weinberg mechanism, and provides a counter example to one of the swampland
conjectures concerning de Sitter vacua in quantum gravity, once string loop effects are taken
into account; it thus paves the way for embedding the Standard Model of particle physics
and cosmology in string theory.

Moduli Stabilization and Inflation in Type IIB/F-theory
In the first part of this talk, a short overview of the ongoing debate on the existence of de Sitter vacua in string theory is presented. In the second part, the moduli stabilisation and inflation are
discussed in the context of type IIB/F-theory. Considering a configuration of three intersecting D7 branes with fluxes, it is shown that higher loop effects inducing logarithmic corrections to
the Kähler potential can stabilise the Kähler moduli in a de Sitter Vacuum. When a new FayetIliopoulos term is included, it is also possible to generate the required number of e-foldings and
satisfy the conditions for slow-roll inflation.

Dual spacetime and nonsingular string cosmology

*: Making use of the T-duality symmetry of superstring theory and of the double geometry from double field theory, we argue that cosmological singularities of a homogeneous and isotropic universe disappear. In fact, an apparent big bang singularity in Einstein gravity corresponds to a universe expanding to infinite size in the dual dimensions.***Abstract***: The singularities which arise at the beginning of time in both standard and inflationary cosmology indicate that the theories which are being used in cosmology break down as the singularity is approached. If space-time is described by Einstein gravity and matter obeys energy conditions which are natural from the point of view of point particle theories, then singularities in homogeneous and isotropic cosmology are unavoidable [1]. These theorems in fact extend to inflationary cosmology [2–4]. But we know that Einstein gravity coupled to point particle matter cannot be the correct description of nature. The quantum structure of matter is not consistent with a classical description of space-time. The early Universe needs to be described by a theory which can unify spacetime and matter at a quantum level. Superstring theory (see e.g., [5,6] for a detailed overview) is a promising candidate for a quantum theory of all four forces of nature. At least at the string perturbative level, the building blocks of string theory are fundamental strings. Strings have degrees of freedom and new symmetries which point particle theories do not have, and these features may lead to a radically different picture of the very early Universe, as discussed many years ago in [7] (see also [8]). As discussed in [7], string thermodynamic considerations indicate that the cosmological evolution in the context of string theory should be nonsingular. A key realization is that the temperature of a gas of closed strings in thermal equilibrium cannot exceed a limiting value, the Hagedorn temperature [9]. In fact, as reviewed in the following section, the temperature of a gas of closed strings in a box of radius R decreases as R becomes much smaller than the string length. If the entropy of the string gas is large, then the range of values of R for which the temperature is close to the Hagedorn temperature TH is large. This is called the “Hagedorn phase” of string cosmology. The exit from the Hagedorn phase is smooth and is a consequence of the decay of string winding modes into string loops.1 The transition leads directly to the radiation phase of standard big bang cosmology (see [11] for reviews of the string gas cosmology scenario). If strings in the Hagedorn phase are in thermal equilibrium, then the thermal fluctuations of the energymomentum tensor can be computed using the methods of [12]. In particular, it can be shown that in a compact space with stable winding modes the specific heat capacity has holographic scaling as a function of the radius of the volume being considered. As a consequence [13,14], thermal fluctuations of strings in the Hagedorn phase lead to a scale-invariant spectrum of cosmological perturbations at late times, with a slight red tilt like what is predicted [15] in inflationary cosmology. If the string scale is comparable to the scale of particle physics grand unification, the predicted amplitude of the fluctuations matches the observations well (see [16] for recent observational results). Hence, string gas cosmology provides an alternative to cosmological inflation as a theory for the origin of structure in the Universe. The predicted spectrum of gravitational waves [17] is also scale invariant, but a slight blue tilt is predicted, in contrast to the prediction in standard inflationary cosmology. This is a prediction by means of which the scenario can be distinguished from standard inflation (meaning inflation in Einstein gravity driven by a matter field obeying the usual energy conditions). A simple modeling of the transition between the Hagedorn phase and the radiation phase leads to a running of the spectrum which is parametrically larger than what is obtained in simple inflationary models [18]. In this paper, we will study the cosmological background dynamics which follow from string theory if the target space has stable winding modes. An example where this is the case is a spatial torus. We will argue that from the point of view of string theory the dynamics is nonsingular.***Introduction**On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude
We consider theories of weakly interacting higher spin particles in flat spacetime. We focus on the four-point scattering amplitude at high energies and imaginary scattering angles. The leading asymptotic of the amplitude in this regime is universal and equal to the corresponding limit of the Veneziano amplitude. In this paper, we find that the first sub-leading correction to this asymptotic is universal as well. We compute the correction using a model of relativistic strings with massive endpoints. We argue that it is unique using holography, effective theory of long strings and bootstrap techniques.

Scattering Amplitudes For All Masses and Spins
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin S particles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called "spinning polynomials". Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin can not be "elementary". The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can't be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g-2) as well as the beta function and rational terms in QCD. "Off-shell" observables like correlation functions and form-factors can be thought of as scattering amplitudes with external "probe" particles of general mass and spin, so all these objects--amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

String Amplitudes from Field-Theory Amplitudes and Vice Versa
We present an integration-by-parts reduction of any massless tree-level string correlator to an equivalence class of

*logarithmic functions*, which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field-theory one and a special disk or sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL(2) weight. By applying the reduction to open bosonic or heterotic strings, we get a closed-form CHY integrand for the (DF)2+Yang−Mills+ϕ3 theory.Dark Energy and String Theory
A radiatively stable de Sitter spacetime is constructed by considering an intrinsically non-commutative and generalized-geometric formulation of string theory, which is related to a family of F-theory models endowed with non-trivial anisotropic axion-dilaton backgrounds. In particular, the curvature of the canonically conjugate dual space provides for a positive cosmological constant to leading order, that satisfies a radiatively stable see-saw-like formula, which in turn induces the dark energy in the observed spacetime. We also comment on the non-commutative phase of the non-perturbative formulations of string theory/quantum gravity implied by this approach.

Dark matter in very supersymmetric dark sectors
If supersymmetry exists at any scale, regardless of whether it is restored around the weak scale, it may be a good symmetry of the dark sector, enforcing a degeneracy between its lowest lying fermions and bosons. We explore the implications of this scenario for the early Universe and dark matter, as well as the corresponding signatures. In particular, we show that the thermal history of the dark-sector results in codecaying dark matter in much of the parameter space. This implies new phenomenological signatures and presents a new way to discover high scale supersymmetry.

Natural SUSY in D-brane Inspired Models
We examine the naturalness of the D-brane inspired model constructed in flipped SU(5) supplemented with vector-like particles at the TeV scale, dubbed flippons. We find the model can produce
a mainly Higgsino-like lightest supersymmetric particle (LSP) and small light stops, as favored by naturalness. In fact, a large trilinear scalar At term at the electroweak (EW) scale creates a large
mass splitting between the top squarks, driving the light stop to near degeneracy with an LSP that is almost all Higgsino, with ∆M(et1, χe 01) < 5 GeV, evading the LHC constraint on et1 → cχe 0
1 thus far. Given the smallness of the light stop, generating a 125 GeV light Higgs boson mass is aided by one-loop contributions from the Yukawa couplings between the flippons and Higgs fields. The resulting parameter space satisfying naturalness is rather constrained, thus we assess its viability by means of comparison to the LHC constraint on soft charm jets and direction detection limits on spin-independent cross-sections. Finally, we compute the level of fine-tuning at both the EW scale and high scale (HS), highlighted by a rich region with ∆EW < 100, i.e., fine-tuning better than 1%.

Emergent Supersymmetry at First-Order Quantum Phase Transition
Supersymmetry, a symmetry between fermions and bosons, provides a promising extension of the
standard model but is still lack of experimental evidence. Recently, the interest in supersymmetry arises in the condensed matter community owing to its potential emergence at the continuous
quantum phase transition. In this letter we demonstrate that 2+1D supersymmetry, relating massive Majorana and Ising fields, can emerge at the first-order quantum phase transition of the Ising
magnetization by tuning a single parameter. We show that the emergence of supersymmetry is accompanied by a topological phase transition for the Majorana field, where its non-zero mass changes the sign but keeps the magnitude. An experimental realization of this scenario is proposed using the surface state of a 3+1D time-reversal invariant topological superconductor with surface magnetic doping.

How Spacetime is Built by Quantum Entanglement via the Gauge/Gravity Duality
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of
a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the
conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime,
reconstructing the local data in the bulk from the entanglement on the boundary. We also show that
positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the
reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by
positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative
entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy
conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an
information theoretical interpretation of the convexity in terms of the Fisher metric.

Classical de Sitter Solutions of Ten-Dimensional Supergravity
We find four-dimensional de Sitter compactifications of type IIA supergravity by directly solving the
ten-dimensional equations of motion. In the simplest examples, the internal space has the topology
of a circle times an Einstein manifold of negative curvature. An orientifold acts on the circle with
two fixed loci, at which an O8− and an O8+ plane sit. These orientifold planes are fully backreacted
and localized. While the solutions are numerical, the charge and tension of the orientifold planes
can be verified analytically. Our solutions have moduli at tree level and can be made parametrically
weakly-coupled and weakly-curved. Their fate in string theory depends on quantum corrections.

Deriving the Inflaton in Compactified M-theory with a De Sitter Vacuum
Compactifying M-theory on a manifold of G2 holonomy gives a UV complete 4D theory.
It is supersymmetric, with soft supersymmetry breaking via gaugino condensation that simultaneously stabilizes all moduli and generates a hierarchy between the Planck and the Fermi
scale. It generically has gauge matter, chiral fermions, and several other important features of our world. Here we show that the theory also contains a successful inflaton, which is a linear
combination of moduli closely aligned with the overall volume modulus of the compactified G2 manifold. The scheme does not rely on ad hoc assumptions, but derives from an effective quantum theory of gravity. Inflation arises near an inflection point in the potential which can be deformed into a local minimum. This implies that a de Sitter vacuum can occur in the moduli
potential even without uplifting. Generically present charged hidden sector matter generates a de Sitter vacuum as well. The resulting quantum theory is UV complete and describes gravity plus the Standard Model plus Higgs physics.

Cosmic Inflation from Supersymmetry Breaking
I discuss the possibility that inflation is driven by supersymmetry breaking, with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry to satisfy the slow-roll conditions, avoiding the so-called η -problem, leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum, describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and, in the simplest case, predict a rather small tensor-to-scalar ratio of primordial perturbations.

Non-Perturbative String Theory from AdS/CFT
The large N expansion of giant graviton correlators is considered. Giant gravitons are
described using operators with a bare dimension of order N. In this case the usual 1/N expansion is not applicable and there are contributions to the correlator that are non-perturbative
in character. By writing the (square of the) correlators in terms of the hypergeometric
function 2F1(a, b; c; 1), we are able to rephrase the 1/N expansion of the correlator as a semiclassical expansion for a Schr¨odinger equation. In this way we are able to argue that the
1/N expansion of the correlator is Borel summable and that it exhibits a parametric Stokes
phenomenon as the angular momentum of the giant graviton is varied.

Towards deriving the AdS/CFT correspondence
I present the sketch of a “physicist’s” derivation of the AdS/CFT correspondence
for the original pair, string theory in AdS5 × S5 vs. N = 4 SYM, based on the
pp wave limit, and deviations from it. I show that one can reverse the logic,
and derive the action of N = 4 SYM, as kinetic terms plus vertices, as well
as the elements of its path integral, from string theory on the pp wave. One
can also treat consistently deviations from the “strings on the pp wave” limit,
starting from the SYM side, and a priori reconstruct the full AdS5×S5 geometry
perturbatively, as well as full perturbative string theory on it.