Correlation Functions of Operators and Wilson Surfaces in the d=6, (0,2) Theory in the Large N Limit

TL;DR

This work analyzes the large-$N$ limit of the six-dimensional (0,2) superconformal theory via its AdS$_7\times S^4$ holographic dual, computing two- and three-point functions of protected chiral primaries and deriving the cubic couplings of the corresponding KK scalars. By mapping KK modes $s^I$ and their interactions to boundary operators $\mathcal{O}^I$, the authors obtain a detailed, gamma-function enhanced expression for the three-point correlators, and they establish the boundary-to-bulk dictionary needed to relate bulk cubic vertices to CFT data. In addition, the paper analyzes the operator product expansion of a spherical Wilson surface, identifying low-dimension, $SO(5)$-singlet operators that can appear and extracting explicit OPE coefficients for the chiral primaries from Wilson-surface correlators. Overall, the results demonstrate how protected 6D CPO data and surface-operator OPE coefficients can be accessed holographically, providing a benchmark for DLCQ formulations and deepening the connection between M5-brane dynamics and AdS/CFT. The findings are significant for understanding nontrivial six-dimensional SCFTs and for extending holographic techniques to higher-dimensional, chiral theories.

Abstract

We compute the two and three-point correlation functions of chiral primary operators in the large N limit of the (0,2), d=6 superconformal theory. We also consider the operator product expansion of Wilson surfaces in the (0,2) theory and compute the OPE coefficients of the chiral primary operators at large N from the correlation functions of surfaces.