Quantum spectral curve for (q,t)-matrix model

TL;DR

This paper derives a quantum spectral curve for the (q,t)-matrix model, revealing its connection to the Baxter TQ equation and the spectral duality with Seiberg-Witten integrable systems in gauge theories.

Contribution

The paper introduces a quantum spectral curve for the (q,t)-matrix model, linking it to integrable systems and gauge theory dualities.

Findings

Quantum spectral curve is a difference equation.

Reproduces Baxter TQ equation in Nekrasov-Shatashvili limit.

Establishes spectral duality with Seiberg-Witten systems.

Abstract

We derive quantum spectral curve equation for (q,t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.