We study the connection between N=2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D -type and discuss how they describe the quantum cohomology of the corresponding Nakajima’s quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix. © 2015 Elsevier B.V.

Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories / Bonelli, G.; Sciarappa, A.; Tanzini, A.; Vasko, P.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 109:Nov(2016), pp. 3-43. [10.1016/j.geomphys.2015.10.001]

Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories

Bonelli, G.;Sciarappa, A.;Tanzini, A.;Vasko, P.
2016-01-01

Abstract

We study the connection between N=2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D -type and discuss how they describe the quantum cohomology of the corresponding Nakajima’s quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix. © 2015 Elsevier B.V.
2016
109
Nov
3
43
https://doi.org/10.1016/j.geomphys.2015.10.001
https://arxiv.org/abs/1505.07116
Bonelli, G.; Sciarappa, A.; Tanzini, A.; Vasko, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11843
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