All high mathematics serves to do is to beget higher mathematics.** ~ Ashim Shanker!**

**~ Ashim Shanker!**Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. W. S. Anglin, in Mathematics and History

In my last post I showed via AdS/CFT analysis, that **gravity is an emergent holographic notion**: namely, that one can holographically derive (logically deduce) gravity from conformal field theoretic **entropic properties of** quantum entanglement, and that such a property is a **necessary condition for the ‘bundle’ existence of the gravitonic field**. To do so, I had to deform CFT by source-fields via the addition of , which is a **dual AdS theory with a bundle field** and a **boundary condition**

with the **conformal dimension**, a local operator and **equals the number of indices** of **substracting the contravariant** ones to get the AdS/CFT quasi-isomorphic Maldacena correspondence ( = AdS/CFT correspondence), thus the identity

with the left-hand side being the **vacuum expectation value of the time-ordered exponential of the operator over CFT**, the right-hand side being **the quantum gravity functional with topological-**c**onformal boundary condition**, thus leading to **holographic emergence, and in a sense, elimination, of gravity**. Recall that the **Heisenberg Uncertainty Relation** holds for **energy and time**, leading to many anomalies for the Green‘s function of **string-propagation**:

with the **Lagragian**, due to the fact the **superpositionality** with respect to **energy** makes **Feynman path-summation**:

**incoherent since some topologies will degenerate and violate existence conditions for** tangent bundles over Minkowski spacetime and **some will not correspond to the categorical CFT-manifold**, and hence we need to replace the Green’s function with the Källén–Lehmann **spectral representation**. This is where the **GKP-Witten Relation** enters with all its glory:

with **background deficit angle** and **the curvature localized on the boundary with an angular deficit**:

with **action**

giving us

with

hence **solving the ‘Ricci/dilaton’ problem** I discussed in my last post, since now the **holographic formula** is

with the ‘magical’ expression ( being the string lenght):

and with that, the GKP-Witten relation solves the ‘Ricci/dilaton’ problem for the action of supergravity theory.

Now let me set up the mathematical context needed to show, in a forthcoming post, that even in M-Theory, or for that matter: any quantum-gravity theory, **one cannot coherently quantize gravity** in a way that satisfies General Relativistic ‘necessity-criteria’ – as I will show that this would imply, **via gravitonic quantum entanglement**, the point-**‘instantaneous’ collapse of spacetime to a zero-dimensional point like** singularity. Not a pretty picture! To do that I have to show that boundary **AdS/CFT admits of a ‘local’ symmetry in the bulk theory that is dual to a ‘global’ symmetry corresponding to the** **boundary** and that the (Gubser-Klebanov-Polyakov)-Witten relation deduces the **Green correlation functions** and that they must have **negative Källén–Lehmann spectral** **representation**

with being the gauge-theoretic positive-definite spectral density function.

In the AdS/CFT duality, one must note that the **second derivative of the on-shell action principle** with respect to the bulk second-quantized field, must, by unitarity, be** identical to the Green** function of the **current**

with being the Euclidean time-ordering, and the Green function.

For equation 1. to be true, the connected Green function should provably reduce to the **static **…

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