Exact Superpotentials, Theories with Flavor and Confining Vacua

Gómez–Reino, Marta

doi:10.1088/1126-6708/2004/06/051

Cited by 13 publications

(23 citation statements)

References 43 publications

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“…The effective superpotential of SU(N c ) theory has been obtained in [24]. Comparison of the effective superpotentials of these two theories provides the following equivalence: 20) which agrees with the relation obtained in [14].…”

Section: T Rφsupporting

confidence: 71%

“…In the following section we apply the method developed in [24] for the SO(N c ) gauge theory with one adjoint matter field and N f fundamental flavors.…”

Section: Relevant Matrix Modelmentioning

confidence: 99%

“…Following the arguments in [24], for the effective superpotential evaluation we can still look at a point in the quantum moduli space of N = 2 pure gauge theory where r = [N c /2] (rank of SO(N c )) monopoles become massless [14]. This corresponds to the point where the Seiberg-Witten curve factorizes completely.…”

Section: Unbroken Gauge Groupmentioning

confidence: 99%

“…For U(N) gauge group, it was shown that the effective superpotential gets contributions from the matrix model planar diagrams with zero or one boundary [20,22]. In [24], it has been shown that the U(N) effective superpotential for theories with N f fundamental flavors can be calculated in terms of quantities computed in the pure gauge theory. Chiral N = 1 U(N) gauge theories with antisymmetric, conjugate symmetric, adjoint and fundamental matter have also been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…We consider N = 1 supersymmetric SO(N c ) gauge theory with arbitrary tree level superpotential of one chiral superfield in the adjoint representation and N f fundamental matter multiplets. We use the technique developed in [24] to calculate the effective superpotential of this theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Effective SO superpotential for N=1 theory with Nf fundamental matter

Borhade

Ramadevi

2007

Nuclear Physics B

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Motivated by the duality conjecture of Dijkgraaf and Vafa between supersymmetric gauge theories and matrix models, we derive the effective superpotential of N = 1 supersymmetric gauge theory with gauge group SO(N c ) and arbitrary tree level polynomial superpotential of one chiral superfield in the adjoint representation and N f fundamental matter multiplets. For a special point in the classical vacuum where the gauge group is unbroken, we show that the effective superpotential matches with that obtained from the geometric engineering approach.

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Section: T Rφsupporting

confidence: 71%

“…In the following section we apply the method developed in [24] for the SO(N c ) gauge theory with one adjoint matter field and N f fundamental flavors.…”

Section: Relevant Matrix Modelmentioning

confidence: 99%

Section: Unbroken Gauge Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Effective SO superpotential for N=1 theory with Nf fundamental matter

Borhade

Ramadevi

2007

Nuclear Physics B

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Matrix model conjecture for exact BS periods and Nekrasov functions

Миронов

Морозов²,

Shakirov

2010

J. High Energ. Phys.

116

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We give a concise summary of the impressive recent development unifying a number of different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric series) form a full basis for all conformal blocks of the Virasoro algebra and are sufficient to provide the same for some (special) conformal blocks of W-algebras. They can be described in terms of Seiberg-Witten theory, with the SW differential given by the 1-point resolvent in the DV phase of the quiver (discrete or conformal) matrix model (β-, where ε and β are related to the LNS parameters ǫ1 and ǫ2. This provides explicit formulas for conformal blocks in terms of analytically continued contour integrals and resolves the old puzzle of the free-field description of generic conformal blocks through the Dotsenko-Fateev integrals. Most important, this completes the GKMMM description of SW theory in terms of integrability theory with the help of exact BS integrals, and provides an extended manifestation of the basic principle which states that the effective actions are the tau-functions of integrable hierarchies. Today it is clear that a new unification of the fundamental importance emerges, bringing together at a principally new level the CFT, the theory of loop algebras, SW theory, quantization theory, Baxter equations, DV phase of matrix models, loop equations, the theory of hypergeometric functions, symmetric groups, Hurwitz theory, Kontsevich models and modern combinatorics. This unification is capable to resolve a number of long-standing problems in each of the fields. The goal of this paper is to briefly summarize our knowledge about this emerging pattern, which is scattered and expressed in length in a number of fresh [29,30], makes the picture complete, resolves the remaining uncertainties (about the shape of the second deformation) in [56,57] and finalizes the program [3] to reformulate SW theory of [1,2] in terms of the BS integrals and underlying integrable systems. We do not discuss long formulas, checks and even evidence in favor of all these conjectures: all calculations in these fields remain long and tedious, and most statements still need to be checked and proved, however, the entire picture is starting to get relatively clear.

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Classical spin chains and exact three-dimensional superpotentials

Boels¹

2005

Nuclear Physics B

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We study exact effective superpotentials of four-dimensional N = 2 supersymmetric gauge theories with gauge group U (N ) and various amounts of fundamental matter on R 3 × S 1 , broken to N = 1 by turning on a classical superpotential for the adjoint scalar. On general grounds these superpotentials can easily be constructed once we identify a suitable set of coordinates on the moduli space of the gauge theory. These coordinates have been conjectured to be the phase space variables of the classical integrable system which underlies the N = 2 gauge theory. The sought low energy effective superpotential can then be constructed from the conserved quantities in the integrable system. For the gauge theory under study these integrable systems are degenerations of the classical, inhomogeneous, periodic SL(2, C) spin chain. Ambiguities in the degeneration provide multiple coordinate patches on the gauge theory moduli space. By studying the vacua of these superpotentials in several examples we find that the spin chain provides coordinate patches that parametrize holomorphically the part of the gauge theory moduli space which is connected to the electric (as opposed to magnetic or baryonic) Higgs and Coulomb branch vacua. The baryonic branch root is on the edge of some coordinate patches. As a product of our analysis all maximally confining (non-baryonic) Seiberg-Witten curve factorizations for N f ≤ N c are obtained, explicit up to one constraint for equal mass flavors and up to two constraints for unequal mass flavors. Gauge theory addition and multiplication maps are shown to have a natural counterpart in this construction. Furthermore it is shown how to integrate in the meson fields in this formulation in order to obtain three and four dimensional Affleck-Dine-Seiberg-like superpotentials.

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Exact Superpotentials, Theories with Flavor and Confining Vacua

Cited by 13 publications

References 43 publications

Effective SO superpotential for N=1 theory with Nf fundamental matter

Effective SO superpotential for N=1 theory with Nf fundamental matter

Matrix model conjecture for exact BS periods and Nekrasov functions

Classical spin chains and exact three-dimensional superpotentials

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