Exact Superpotentials from Matrix Models

Dorey, Nick; Hollowood, Timothy J.; Kumar, S. Prem; Sinkovics, Annamaria

doi:10.1088/1126-6708/2002/11/039

Cited by 77 publications

(151 citation statements)

References 19 publications

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“…This is also what the original discussion of the role of the integrable system in N = 2 theories in four dimensions implies [7,8]. Therefore, we conjecture, following [20,21,22] that the quantum superpotential can be obtained from the classical one by the rule…”

Section: The Proposalsupporting

confidence: 59%

Nonperturbative Superpotentials and Compactification to Three Dimensions

Boels¹,

Duivenvoorden²,

Wijnhout³

2004

J. High Energy Phys.

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We consider four-dimensional N = 2 supersymmetric gauge theories with gauge group U (N ) on R 3 ×S 1 , in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U (N ) to U (tN ), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R 3 × S 1 appears to involve a novel kind of mirror symmetry.

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Section: The Proposalsupporting

confidence: 59%

Nonperturbative Superpotentials and Compactification to Three Dimensions

Boels¹,

Duivenvoorden²,

Wijnhout³

2004

J. High Energy Phys.

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“…Curiously, such a gluing condition defines a Riemann surface of genus one; any significance of this to the physical problem at hand is unclear. Very similar "gluing problems" arise as solutions to large-N holomorphic matrix models in very different contexts [42][43][44][45].…”

Section: Jhep11(2011)138mentioning

confidence: 99%

Weak coupling large-N transitions at finite baryon density

Hollowood

Kumar

Myers

2011

J. High Energ. Phys.

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We study thermodynamics of free SU(N ) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (∼ e N ) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.

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“…The conjecture was initially tested for N = 2 SU(N) gauge theories softly broken to N = 1 by a tree-level superpotential for the adjoint chiral superfields [1] and for the N = 1 * deformation of N = 4 SU(N) SYM [3,4,5]. The conjecture has since been extended to a number of other cases [2,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and has been derived from SU(N) gauge theory [27,28,29].…”

Section: Introductionmentioning

confidence: 99%

Unoriented strings, loop equations, andN=1superpotentials from matrix models

et al. 2003

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We apply the proposal of Dijkgraaf and Vafa to analyze N = 1 gauge theory with SO(N) and Sp(N) gauge groups with arbitrary tree-level superpotentials using matrix model techniques. We derive the planar and leading non-planar contributions to the large M SO(M) and Sp(M) matrix model free energy by applying the technology of higher-genus loop equations and by straightforward diagrammatics. The loop equations suggest that the RP 2 free energy is given as a derivative of the sphere contribution, a relation which we verify diagrammatically. With a refinement of the proposal of Dijkgraaf and Vafa for the effective superpotential, we find agreement with field theory expectations.

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Exact Superpotentials from Matrix Models

Cited by 77 publications

References 19 publications

Nonperturbative Superpotentials and Compactification to Three Dimensions

Nonperturbative Superpotentials and Compactification to Three Dimensions

Weak coupling large-N transitions at finite baryon density

Unoriented strings, loop equations, andN=1superpotentials from matrix models

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