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Title:
Gauge theories and quantum hydrodynamics
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Abstract:
Hydrodynamic integrable systems are described in terms of integrable partial differential equations. I will focus on the periodic Intermediate Long Wave (ILW) system, both at the classical and quantum level. The quantum problem has not been solved yet, if not in a particular limit (the Benjamin-Ono limit) which is related to the AGT correspondence. I will show how a particular two dimensional N=(2,2) gauge theory on S^2 can be used to determine the spectrum of the ILW system via Bethe Ansatz equations, as well as the norm of the eigenstates. Moreover the partition function of this theory computes genus zero Gromov-Witten invariants for the instanton moduli space, thus relating quantum cohomology to quantum hydrodynamics.
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