Mordell integrals and Giveon-Kutasov duality

We solve, for finite \(N\), the matrix model of supersymmetric \(U(N)\) Chern-Simons theory coupled to \(N_{f}\) massive hypermultiplets of \(R\)-charge \(\frac{1}{2}\), together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix,...

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Bibliographic Details
Published in:arXiv.org 2016-01
Main Authors: Giasemidis, Georgios, Tierz, Miguel
Format: Article
Language:English
Subjects:
Field theory (physics)
Flavors
Integrals
Mathematical models
Partitions
Partitions (mathematics)
Quantum theory
Supersymmetry
Online Access:Get full text
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Summary:We solve, for finite \(N\), the matrix model of supersymmetric \(U(N)\) Chern-Simons theory coupled to \(N_{f}\) massive hypermultiplets of \(R\)-charge \(\frac{1}{2}\), together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order \(N_{f}-1\)) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the \(\mathcal{N}=3\) setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to \(N_{f}=12\) flavours).
ISSN:2331-8422
DOI:10.48550/arxiv.1511.00203