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Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

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arxiv 1510.00972 v2 pith:NYHQAMTD submitted 2015-10-04 hep-th math-phmath.MPmath.QA

Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

classification hep-th math-phmath.MPmath.QA
keywords quantumgaugehydrodynamicalintegrablemany-bodysupersymmetricsystemstheories
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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.

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    Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bund...