Exact quantization conditions for the elliptic Ruijsenaars-Schneider model

TL;DR

This paper establishes exact quantization conditions for the elliptic Ruijsenaars-Schneider model, linking it to five-dimensional supersymmetric gauge theories, and emphasizes the role of non-perturbative effects and dualities.

Contribution

It introduces and tests new exact quantization conditions for the elliptic Ruijsenaars-Schneider system based on gauge theory correspondence and explores duality and non-perturbative corrections.

Findings

Validated quantization conditions through tests against known results.

Highlighted the significance of non-perturbative corrections.

Connected eigenfunction problems to gauge theory via Separation of Variables.

Abstract

We propose and test exact quantization conditions for the $N$-particle quantum elliptic Ruijsenaars-Schneider integrable system, as well as its Calogero-Moser limit, based on the conjectural correspondence to the five-dimensional $\mathcal{N} = 1$ $SU(N)$ gauge theory in the Nekrasov-Shatashvili limit. We discuss two natural sets of quantization conditions, related by the electro-magnetic duality, and the importance of non-perturbative corrections in the Planck constant. We also comment on the eigenfunction problem, by reinterpreting the Separation of Variables approach in gauge theory terms.