Solution of N=2 Gauge Theories via Compactification to Three Dimensions

Details Solution of N=2 Gauge Theories via Compactification to Three Dimensions Solution of N=2 Gauge Theories via Compactification to Three Dimensions

1998-04-09

arxiv.org/abs/hep-th/9804069v1

Nucl.Phys. B534 (1998) 531-545

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX

Scientific paper

10.1016/S0550-3213(98)00520-3

A number of N=2 gauge theories can be realized by brane configurations in Type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a subclass of these theories (elliptic models). We observe that upon compactification on a circle one can use a version of mirror symmetry to map the original brane configuration into one containing only D-branes. Simultaneously the Coulomb branch of the four-dimensional theory is mapped to the Higgs branch of a five-dimensional theory with three-dimensional impurities. The latter does not receive quantum corrections and can be analyzed exactly. The solution is naturally formulated in terms of an integrable system, which is a version of a Hitchin system on a punctured torus.

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