Exact superpotentials for theories with flavors via a matrix integral

Argurio, Riccardo; Campos, Vanicson L.; Ferretti, Gabriele; Heise, Rainer

doi:10.1103/physrevd.67.065005

Cited by 76 publications

(145 citation statements)

References 20 publications

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“…The fact that in the results presented in [30] the dependence on the glueball superfield enters in a highly non-linear way in the JHEP06 (2004)051 equation for the effective superpotential, makes it very complicated to compare both results. Nevertheless, we can check our result by comparing it with the one obtained in [10] for the particular case of a quadratic tree level superpotential, W tree = 1 2 trΦ 2 . For this particular case we have that g 2 = 1, g n = 0, n = 2.…”

Section: The Matter Contributionmentioning

confidence: 99%

“…In the generalization of this proposal to include fields in the fundamental representation of the gauge group (this case was first considered in [10]) this superpotential is given by…”

Section: Theories With Flavors From Matrix Modelsmentioning

confidence: 99%

“…The exact effective superpotential was computed in [17] for a pure gauge theory using the "integrating in" procedure. The addition of fundamental matter was considered in [10,33] for the particular case of a quadratic tree level superpotential, W tree = 1 2 trΦ 2 , and in [30], using random matrix models, for a more general tree level superpotential. The method described in this section shows that in order to obtain the exact superpotential with fundamental matter in the maximally degenerating point of the moduli space we just need to compute, within the matrix model formulation, vacuum expectation values of several operators.…”

Section: Jhep06(2004)051mentioning

confidence: 99%

“…This proposal provides direct connections between the computations in the matrix model descriptions with those in supersymmetric gauge theories. The proposal was later extended to the addition of matter in the fundamental representation of the gauge group in [10]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…Actually there has been significant work on using the Dijkgraaf-Vafa proposal to get results of N = 2 theories [14,16]- [21] In the case of N = 1 theories with fundamental matter the effective superpotential will have contributions coming from planar diagrams with one boundary, apart from the contribution coming from the planar diagrams with no boundaries [10]. As we will see in the first part of the paper, those contributions to the superpotential can be computed, within the matrix model setup, in terms of traces of certain matrix model operators.…”

Section: Introductionmentioning

confidence: 99%

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Exact Superpotentials, Theories with Flavor and Confining Vacua

Gómez–Reino

2004

J. High Energy Phys.

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In this paper we study some interesting properties of the effective superpotential of N = 1 supersymmetric gauge theories with fundamental matter, with the help of the Dijkgraaf-Vafa proposal connecting supersymmetric gauge theories with matrix models. We find that the effective superpotential for theories with N f fundamental flavors can be calculated in terms of quantities computed in the pure (N f = 0) gauge theory. Using this property we compute in a remarkably simple way the exact effective superpotential of N = 1 supersymmetric theories with fundamental matter and gauge group SU(N c ), at the point in the moduli space where a maximal number of monopoles become massless (confining vacua). We extend the analysis to a generic point of the moduli space, and show how to compute the effective superpotential in this general case.

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Section: The Matter Contributionmentioning

confidence: 99%

“…In the generalization of this proposal to include fields in the fundamental representation of the gauge group (this case was first considered in [10]) this superpotential is given by…”

Section: Theories With Flavors From Matrix Modelsmentioning

confidence: 99%

Section: Jhep06(2004)051mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Superpotentials, Theories with Flavor and Confining Vacua

Gómez–Reino

2004

J. High Energy Phys.

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Multi-Trace Superpotentials vs. Matrix Models

Balasubramanian

Feng²,

He³

et al. 2003

Commun. Math. Phys.

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We consider N = 1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multi-trace tree-level superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the single-trace case, holomorphy and symmetries do not forbid non-planar contributions. Nevertheless, only a special subset of the planar diagrams contributes to the exact result. Some of the data of this subset can be computed from the large-N limit of an associated multi-trace Matrix model. However, the prescription differs in important respects from that of Dijkgraaf and Vafa for single-trace superpotentials in that the field theory effective action is not the derivative of a multi-trace matrix model free energy. The basic subtlety involves the correct identification of the field theory glueball as a variable in the Matrix model, as we show via an auxiliary construction involving a single-trace matrix model with additional singlet fields which are integrated out to compute the multi-trace results. Along the way we also describe a general technique for computing the large-N limits of multi-trace Matrix models and raise the challenge of finding the field theories whose effective actions they may compute. Since our models can be treated as N = 1 deformations of pure N =2 gauge theory, we show that the effective superpotential that we compute also follows from the N = 2 Seiberg-Witten solution. Finally, we observe an interesting connection between multi-trace local theories and non-local field theory.Comment: 35 pages, LaTeX, 6 EPS figures. v2: typos fixed, v3: typos fixed, references added, Sec. 5 added explaining how multi-trace theories can be linearized in traces by addition of singlet fields and the relation of this approach to matrix model

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