M5-branes and Wilson Surfaces in AdS$_{7}$/CFT$_{6}$ Correspondence

Abstract

We study AdS$_{7}$/CFT$_{6}$ correspondence between M-theory on AdS$_{7} \times S^{4}$ and the 6D $\mathcal{N} = (2,0)$ superconformal field theory. In particular we focus on Wilson surfaces. We use the conjecture that the (2,0) theory compactified on $S^{1}$ is equivalent to the 5D maximal super Yang-Mills (MSYM) and Wilson surfaces wrapping this $S^1$ correspond to Wilson loops in 5D MSYM. The Wilson loops in 5D MSYM obtained by the localization technique result in the Chern-Simons matrix model. We calculate the expectation values of Wilson surfaces in large rank symmetric representations and anti-symmetric representations by using this result. In the gravity side, the expectation values for probe M5-branes wrapping submanifolds of the background are computed. Consequently we find new, non-trivial evidence for the AdS$_{7}$/CFT$_{6}$ correspondence that the results in the gravity side perfectly agree with those in the CFT side.