Super-Spin Chains for 6D SCFTs

TL;DR

This paper extends the integrable spin chain description of operator mixing in 6D SCFTs to the full superconformal algebra, providing Bethe ansatz equations and identifying closed subsectors, with implications for related theories.

Contribution

It generalizes the spin chain framework from a protected subsector to the entire superconformal algebra in 6D SCFTs, including Bethe ansatz solutions.

Findings

Derived Bethe ansatz equations for the super-spin chain.

Identified subsectors closed under operator mixing.

Extended analysis to 6D little string theories and 4D SCFTs.

Abstract

Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$ is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver structures.