Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms

Russo, Jorge G.; Silva, Guillermo A.

doi:10.48550/arxiv.1510.02957

Cited by 4 publications

(9 citation statements)

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“…For integer k, in some cases the partition function on S 3 has a finite number of terms (see [23,24,25,26,27,28] for many examples). This can be illustrated by U(1) N = 2 Chern-Simons theory with a FI deformation, coupled to a pair of massless chiral fields of ∆ = 1/2 and opposite gauge charges.…”

Section: U (1) × U (1) Abjm Theory With Fi and Mass Deformationsmentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ Chern-Simons-matter theories without vortices

Russo¹,

Schaposnik²

2017

J. High Energ. Phys.

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We study N = 2 Chern-Simons-matter theories with gauge group U k 1 (1) × U k 2 (1). We find that, when k 1 + k 2 = 0, the partition function computed by localization dramatically simplifies and collapses to a single term. We show that the same condition prevents the theory from having supersymmetric vortex configurations. The theories include mass-deformed ABJM theory with U(1) k ×U −k (1) gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group U k 1 (1)×· · ·×U k N (1).

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Section: U (1) × U (1) Abjm Theory With Fi and Mass Deformationsmentioning

confidence: 99%

N = 2 $$ \mathcal{N}=2 $$ Chern-Simons-matter theories without vortices

Russo¹,

Schaposnik²

2017

J. High Energ. Phys.

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“…Notice that there seem to be apparent poles at m = iπ/k and, even though masses are real, one can still look for poles or zeros of the partition function on the complex plane, see [25,26] for example. As we shall see below with more cases, these supposed poles seem to appear for m = 2iπ/k for N f even and m = iπ/k for odd N f .…”

Section: Analytical Expressions For the Partition Functions And Some ...mentioning

confidence: 99%

Mordell integrals and Giveon-Kutasov duality

Giasemidis

Tierz

2016

J. High Energ. Phys.

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We solve, for finite N , the matrix model of supersymmetric U(N ) ChernSimons theory coupled to N f massive hypermultiplets of R-charge 1 2 , together with a FayetIliopoulos 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 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).

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“…It was first studied at large N in [21] (with Fayet-Iliopoulos parameter ς = 0). The model is [22,23] (3.1)…”

Section: Weak Coupling Limit and Meixner-pollaczek Polynomialsmentioning

confidence: 99%

“…This extension of the ABJM matrix model actually also includes a Fayet-Iliopoulos parameter ς, which has been repackaged with the mass term deformation as m 1 = m + ς and m 2 = m − ς [22,23].…”

Section: Weak Coupling Limit and Meixner-pollaczek Polynomialsmentioning

confidence: 99%

Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators

Tierz

2016

Preprint

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We give explicit analytical expressions for the partition function of U (N ) k × U (N + M ) −k ABJ theory at weak coupling (k → ∞) for finite and arbitrary values of N and M (including the ABJM case and its mass-deformed generalization). We obtain the expressions by identifying the one-matrix model formulation with a Meixner-Pollaczek ensemble and using the corresponding orthogonal polynomials, which are also eigenfunctions of a su(1, 1) quantum oscillator. Wilson loops in mass-deformed ABJM are also studied in the same limit and interpreted in terms of su(1, 1) coherent states. 7 The one boson realization only allows for Bargmann index λ = 1/4 or λ = 3/4. 8 Thanks to Jorge Russo for pointing this out.

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Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms

Cited by 4 publications

References 0 publications

N = 2 $$ \mathcal{N}=2 $$ Chern-Simons-matter theories without vortices

N = 2 $$ \mathcal{N}=2 $$ Chern-Simons-matter theories without vortices

Mordell integrals and Giveon-Kutasov duality

Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators

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