6D SCFTs, 4D SCFTs, conformal matter, and spin chains

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 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 C-2/Z(K) singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg XXXs=1/2 spin chain with open boundary conditions, and similar considerations hold for its T-2 reduction to a 4D 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, spin chain with s > 1/2. We also briefly discuss some generalizations to other operator sectors as well as little string theories. (C) 2021 The Author(s). Published by Elsevier B.V.