Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-11-04
JHEP 0312 (2003) 023
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, JHEP3, 4 figures, improved readility of figures, added references
Scientific paper
10.1088/1126-6708/2003/12/023
We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surface--a set-up that is natural in Witten's M-theory construction of N=2 theories. We then show that the curve can be interpreted as the spectral curve of an integrable system which generalizes the N-body elliptic Calogero-Moser and Ruijsenaars-Schneider systems in that both the positions and momenta take values in compact spaces. It turns out that the resulting system is not simply doubly elliptic, rather the positions and momenta, as two-vectors, take values in the ambient abelian surface. We analyze the two-body system in some detail. The system we uncover provides a concrete realization of a Beauville-Mukai system based on an abelian surface rather than a K3 surface.
Braden Harry W.
Hollowood Timothy J.
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