6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains

TL;DR

This paper explores the connection between 6D and 4D superconformal field theories, revealing that certain operator mixing phenomena can be modeled by integrable spin chains, with implications for understanding their structure and dynamics.

Contribution

It demonstrates that operator mixing in these theories is described by integrable spin chains, extending known results to theories with conformal matter and more general singularities.

Findings

Operator mixing in 6D SCFTs is captured by Heisenberg XXX spin chains.

Large R-charge sectors allow operator dimensions to be studied via spin chain models.

The approach applies to theories from M5-branes probing singularities, including D- and E-type.

Abstract

Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a $\mathbb{C}^{2}/\mathbb{Z}_{K}$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XXX_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XXX_{s}$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories.