Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves

Abstract

Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg-Witten curves (and associated Seiberg-Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U(N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in ref. [hep-th/0303268]. Moreover, in the matrix model for the U(N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg-Witten theory obtained using M-theory methods.

40 pages; v2: reference added; v3: minor typo fixed; v4: clarifying footnote added; published version

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Cited by in corpus (15)

• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Supersymmetric Gauge Theories with Flavors and Matrix Models
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chiral field theories, Konishi anomalies and matrix models
• The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems
• Improved matrix-model calculation of the N=2 prepotential
• Remarks on the analytic structure of supersymmetric effective actions
• More on N=1 Matrix Model Curve for Arbitrary N
• Effective superpotential for U(N) with antisymmetric matter
• Konishi Anomalies and Curves without Adjoints
• Quantum Geometries of $A_2$