AdS/CFT Correspondence And Topological Field Theory

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.