Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-04-07
JHEP 0403:009,2004
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 45 pages, uses AmsMath, minor correction, reference added
Scientific paper
10.1088/1126-6708/2004/03/009
We consider four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U(N) to U(tN), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R^3 x S^1 appears to involve a novel kind of mirror symmetry.
Boels Rutger
Boer Jan de
Duivenvoorden Robert
Wijnhout Jeroen
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