Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

TL;DR

This paper explores the deep connections between quantum hydrodynamical systems and integrable many-body models, revealing their roles in supersymmetric gauge theories and instanton counting through string theory dualities.

Contribution

It establishes a novel correspondence between hydrodynamical systems and integrable models in the context of supersymmetric gauge theories, including spectral matching.

Findings

Hydrodynamical systems describe quantum cohomology and K-theory of instanton moduli spaces.

Integrable many-body models relate to instanton counting in supersymmetric theories.

Energy spectra are matched between hydrodynamical and many-body systems.

Abstract

We study the connection between periodic finite-difference Intermediate Long Wave hydrodynamical systems and integrable many-body models of Calogero and Ruijsenaars-type. The former describe quantum cohomology and quantum K-theory of the ADHM moduli space of Abelian instantons, while the latter arise in the the instanton counting in four and five dimensional supersymmetric gauge theories with eight supercharges in the presence of defects. Using string theory dualities we provide correspondences between hydrodynamical and many-body integrable systems. In particular, we match the energy spectra on both sides.