Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and \Omega-deformed Seiberg-Witten prepotential

TL;DR

This paper explores the connection between Baxter's T-Q equation in spin-chain models and 4D =2 superconformal field theories, revealing a duality between different gauge groups through spectral curves and Seiberg-Witten theory.

Contribution

It demonstrates how a single Baxter's T-Q equation encodes two distinct superconformal field theories with different gauge groups, establishing a novel SU(N)/SU(2)^{N-3} correspondence.

Findings

Spectral curves encode dual gauge theories

Seiberg-Witten differential supports the correspondence

Baxter's T-Q equation captures both theories simultaneously

Abstract

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above different gauge groups are encoded simultaneously in one Baxter's T-Q equation which captures their spectral curves. For example, while one is SU(N_c) with N_f=2N_c flavors the other turns out to be SU(2)^{N_c-3} with N_c hyper-multiplets (N_c > 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.