This post is on the String-String Duality. In particular, the D=6 string-string duality, which is crucial since it allows interchanging the roles of 4-D spacetime and string-world-sheet loop expansion, and this is mathematically essential for phenomenologically adequate string-compactifications. Here I will prove an equivalence between K3 membrane action and orbifold action and show how it entails D=6 string-string duality. Working in the bosonic sector, the membrane action is:

where:

Recall I derived, via Clifford algebraic symmetry, the total action:

which is deep since Clifford algebras are a quantization of exterior algebras, and applying to the ‘Einstein-Minkowski’ tangent bundle, we get via Gaussian matrix elimination, an expansion of via Green-functions, that yields M-Theory’s action:

with the kappa symmetry term. With the metric on , and the corresponding coordinates with an antisymmetric 3-tensor. The worldvolume is:

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