Spin chains for ADE quiver theories

TL;DR

This paper investigates the spectral problem of 4d N=2 ADE quiver gauge theories by mapping them to restricted spin chains, computing the one-loop dilatation operator, and analyzing their protected spectra.

Contribution

It extends the study of spin chains associated with superconformal quiver theories to ADE types, constructs the Bethe ansatz, and evaluates the superconformal index at large N.

Findings

Derived the one-loop dilatation operator for ADE quivers.

Constructed the 2-magnon Bethe ansatz for holomorphic states.

Computed the superconformal index to analyze protected spectra.

Abstract

The spectral problem of four-dimensional superconformal quiver gauge theories can be mapped to one-dimensional spin chains with restricted Hilbert spaces, where the composition of neighbouring spins follows the path algebra of the quiver. To better understand such spin chains, we compute the one-loop planar dilatation operator for the 4d N=2 ADE quiver gauge theories obtained by orbifolding the N=4 Super-Yang-Mills theory and marginally deforming by independently varying the gauge couplings. This extends previous work which was mainly focused on the Z2 quiver. We characterise the general features of the resulting ADE spin-chain models and construct the 2-magnon Bethe ansatz for holomorphic states. We also evaluate, at large N, the N=2 superconformal index of these gauge theories and use it to study their protected spectrum in specific sectors.