AdS/CFT Correspondence And Topological Field Theory

TL;DR

This paper explores the relationship between AdS/CFT correspondence and topological field theories, revealing how magnetic fluxes in super Yang-Mills are represented in higher-dimensional topological theories.

Contribution

It introduces a novel connection between four-dimensional super Yang-Mills theory, five-dimensional Chern-Simons topological field theory, and six-dimensional conformal blocks.

Findings

Magnetic flux in super Yang-Mills corresponds to topological data in 5D theory.

A 7D topological theory governs conformal blocks of 6D CFT.

The framework links gauge theory fluxes to topological invariants.

Abstract

In ${\cal N}=4$ super Yang-Mills theory on a four-manifold $M$, one can specify a discrete magnetic flux valued in $H^2(M,\Z_N)$. This flux is encoded in the AdS/CFT correspondence in terms of a five-dimensional topological field theory with Chern-Simons action. A similar topological field theory in seven dimensions governs the space of ``conformal blocks'' of the six-dimensional $(0,2)$ conformal field theory.