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

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

2003-05-30

arxiv.org/abs/hep-th/0305263v4

Nucl.Phys. B674 (2003) 37-79

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.nuclphysb.2003.09.028

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.

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