Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories

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• 作者：Giulio Bonelli ^{bonelli@sissa.it" class="auth_mail" title="E-mail the corresponding author} ; Antonio Sciarappa ; ^{asciara@sissa.it" class="auth_mail" title="E-mail the corresponding author} ; Alessandro Tanzini ^{tanzini@sissa.it" class="auth_mail" title="E-mail the corresponding author} ; Petr Vasko ^{vaskop@sissa.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Instanton counting ; Quantum cohomology ; Integrable systems
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：109
• 期：Complete
• 页码：3-43
• 全文大小：840 K

文摘

We study the connection between N=2$\mathcal{N}=2$ supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A$A$ and D$D$-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.