Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories

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. *

Explicit examples of DIM constraints for network matrix models

“…In the level one representation it gives elliptic Ruijsenaars Hamiltonian, while in the second level representation it is the difference version of the intermediate long-wave Hamiltonian [197][198][199][200][201][202], which itself is a generalization of the Benjamin-Ono system.…”

Toric Calabi-Yau threefolds as quantum integrable systems. ℛ $$ \mathrm{\mathcal{R}} $$ -matrix and ℛ T T $$ \mathrm{\mathcal{R}}\mathcal{T}\mathcal{T} $$ relations

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