6D large charge and 2D Virasoro blocks

Abstract

We compute observables in the interacting rank-one 6D N=(2,0) superconformal field theory (SCFT) at large R-charge. We focus on correlators involving Φn, namely symmetric products of the bottom component of the supermultiplet containing the stress tensor. By using the moduli space effective action and methods from the large-charge expansion, we compute the operator product expansion coefficients ⟨ΦnΦmΦn+m⟩ in an expansion in 1/n. The coefficients of the expansion are only partially determined from the 6D perspective, but we manage to fix them order-by-order in 1/n numerically by utilizing the 6D/2D correspondence. This is made possible by the fact that this 6D observable can be extracted in 2D from a specific double-scaling limit of the vacuum Virasoro block, which can be efficiently computed numerically. We also extend the computation to higher-rank SCFTs, and discuss various applications of our results to 6D as well as 2D. Published by the American Physical Society 2025