Baryons, boundaries and matrix models

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.

show abstract

“…The same observation about crosscap contributions was made in [35] and more recently for boundaries in [45].…”

Section: )supporting

confidence: 75%

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

et al. 2003

View full text Add to dashboard Cite

show abstract

“…which follows from (14), using (13), (12). At this point, it is useful to recall the corresponding result for SU (N ) (or U (N ) with even potential) [16] …”

Section: Exact So(n ) Superpotential From Factorized Sw Curvementioning

confidence: 91%

SO(N) superpotential, Seiberg–Witten curves and loop equations

Janik¹,

Obers²

2003

Physics Letters B

View full text Add to dashboard Cite

We consider the exact superpotential of N = 1 super Yang-Mills theory with gauge group SO(N ) and arbitrary tree-level polynomial superpotential of one adjoint Higgs field. A field-theoretic derivation of the glueball superpotential is given, based on factorization of the N = 2 Seiberg-Witten curve. Following the conjecture of Dijkgraaf and Vafa, the result is matched with the corresponding SO(N ) matrix model prediction. The verification involves an explicit solution of the first non-trivial loop equation, relating the spherical free energy to that of the non-orientable surfaces with topology RP 2 .

show abstract

“…However, we are interested in the periods computed in the (x, y) coordinates and thus the cutoff in the u-plane should be derived from a more fundamental cutoff in the x-plane. The two cutoffs are related by (30); thus, the period integral defining Π for finite mass for the adjoint field is:…”

Section: Effective Superpotential At Strong Couplingmentioning

confidence: 99%

“…The case of fields in the fundamental representation was discussed extensively in [20]- [39] (see also [40] for progress in other directions), in general without reference to any possible string theory realization of such theories 1 . It turns out that the matrix/gauge theory relation implies that the flavor contribution to the effective superpotential is exactly taken into account by the one-boundary free energy of the corresponding matrix model [21,25,30,37].…”

Section: Introductionmentioning

confidence: 99%

“…An attempt to handle this case was introduced in [24] and requires the introduction of delta functions relating the matrix model flavor fields with the corresponding gauge theory mesons. An alternate suggestion was presented in [30] and involves deforming the naive matrix model by mass terms for all massless fields and then computing the superpotential from the one-boundary free energy. The gauge theory superpotential is obtained by integrating in, in the gauge theory sense, the fields that were originally massless and then taking the massless limit.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Massless flavor in geometry and matrix models

2003

Self Cite

View full text Add to dashboard Cite

The proper inclusion of flavor in the Dijkgraaf-Vafa proposal for the solution of N = 1 gauge theories through matrix models has been subject of debate in the recent literature. We here reexamine this issue by geometrically engineering fundamental matter with type IIB branes wrapped on non-compact cycles in the resolved geometry, and following them through the geometric transition. Our approach treats massive and massless flavor fields on equal footing, including the mesons. We also study the geometric transitions and superpotentials for finite mass of the adjoint field. All superpotentials we compute reproduce the field theory results. Crucial insights come from T-dual brane constructions in type IIA.

show abstract

Baryons, boundaries and matrix models

Cited by 31 publications

References 45 publications

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

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

SO(N) superpotential, Seiberg–Witten curves and loop equations

Massless flavor in geometry and matrix models

Contact Info

Product

Resources

About