Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

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.

49 pages, 7 figures, minor corrections

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• Quantum toroidal algebras and solvable structures in gauge/string theory
• Toroidal q-Opers
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• The non-chiral intermediate Heisenberg ferromagnet equation
• Quasi-Hopf twist and elliptic Nekrasov factor
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence