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Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories

Benini, Francesco
•
Park, D. S.
•
Zhao, P.
2015
  • journal article

Periodico
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Abstract
We interpret certain Seiberg-like dualities of two-dimensional N=(2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kahler moduli space of manifolds constructed from the corresponding Kahler quotients. We study the S^2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor whose physical origin and consequences we spell out in detail. We also present similar dualities in N=(2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.
DOI
10.1007/s00220-015-2452-3
WOS
WOS:000360993800002
Archivio
http://hdl.handle.net/20.500.11767/32553
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84941424655
https://arxiv.org/abs/1406.2699
https://link.springer.com/article/10.1007/s00220-015-2452-3
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Data di acquisizione
Jun 14, 2022
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