Anti-de Sitter space from supersymmetric gauge theory

TL;DR

This paper constructs a four-dimensional supersymmetric gauge theory with classical vacua corresponding to anti-de Sitter space, providing a topological and lattice framework for non-perturbative analysis.

Contribution

It introduces a novel supersymmetric Yang-Mills theory with a topological structure that models anti-de Sitter space and allows for a gauge-invariant lattice formulation.

Findings

Classical vacua correspond to AdS space

Partition function is background-independent

Lattice construction enables non-perturbative studies

Abstract

We construct a four dimensional Yang-Mills theory with ${\cal N}=4$ 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.