Anti-de Sitter space from supersymmetric gauge theory

Abstract

We construct a four dimensional Yang-Mills theory with $\mathcal{N}=4$ twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin connection which is used to enforce local Lorentz invariance. The imaginary part of the connection can then be interpreted as a vierbein. The topological construction ensures that the partition function and classical vacua are independent of the background geometry. Additionally a supersymmetric and gauge invariant lattice construction is possible yielding a non-perturbative definition of the theory.

arXiv comment14 pages. References added. Typos corrected

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