Multi-Trace Superpotentials vs. Matrix Models

Abstract

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.

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 models

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Cited by in corpus (18)

• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Local string models of soft supersymmetry breaking
• On the Matter of the Dijkgraaf--Vafa Conjecture
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Phases of N=1 Supersymmetric Gauge Theories with Flavors
• Cubic curves from matrix models and generalized Konishi anomalies
• Note on Matrix Model with Massless Flavors
• Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacua
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• Gravity without averaging
• Note on Seiberg Duality in Matrix Model
• Matrix Models, Monopoles and Modified Moduli
• Modular Matrix Models
• The Glueball Superpotential for G_2
• Aspects of Supersymmetric Gauge Theory and String Theory
• Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves
• Factorization of Seiberg-Witten Curves with Fundamental Matter
• On the planar free energy of matrix models