(2,0) Superconformal OPEs in D=6, Selection Rules and Non-renormalization Theorems

TL;DR

This paper investigates the operator product expansion of 1/2 BPS operators in six-dimensional (2,0) superconformal field theory, deriving selection rules and non-renormalization theorems with implications for M5 brane dynamics and AdS/CFT correspondence.

Contribution

It constructs all possible three-point functions involving 1/2 BPS operators and long operators, establishing superconformal symmetry constraints and deriving new non-renormalization theorems.

Findings

Derived selection rules for operator interactions.

Established non-renormalization theorems for certain correlators.

Interpreted extremal correlators via protected operator exchange.

Abstract

We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by constructing all possible three-point functions that they can form with another, in general long operator. Such three-point functions are uniquely determined by superconformal symmetry. Selection rules are derived, which allow us to infer ``non-renormalization theorems'' for an abstract superconformal field theory. The latter is supposedly related to the strong-coupling dynamics of $N_c$ coincident M5 branes, dual, in the large-$N_c$ limit, to the bulk M-theory compactified on AdS$_7 \times$S$_4$. An interpretation of extremal and next-to-extremal correlators in terms of exchange of operators with protected conformal dimension is given.