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

TL;DR

The paper develops a detailed, symmetry-driven analysis of the OPE for two $\frac{1}{2}$ BPS operators in the 6D $(2,0)$ SCFT, showing that superconformal constraints fix three-point functions and enforce selection rules that identify protected (BPS/semishort) exchanges in the OPE. By organizing the operator spectrum via $OSp(8^{*}/4)$ representations and harmonic superspace, the authors derive explicit conditions on the third operator and demonstrate how extremal and next-to-extremal correlators factorize and remain non-renormalized, consistent with AdS$_7$/CFT$_6$ expectations for M5-brane dynamics on $AdS_7\times S^4$. The results reveal a “field theory of 1/2 BPS operators,” where extremal correlators involve only BPS exchanges and next-to-extremal correlators are protected despite the presence of semishort operators in the OPE. Overall, the work provides a robust, OPE-based framework for non-renormalization and extremal correlator phenomena in six-dimensional superconformal theories, with potential generalizations to other $D=6$ algebras and related dimensions.

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.