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The curve of compactified 6D gauge theories and integrable systems / Harry W. Braden; Timothy Hollowood

Journal of High Energy Physics, Volume: "12", Issue: 12, Pages: 023 - 023

Swansea University Author: Timothy, Hollowood

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Abstract

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 surfa...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2003
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28534
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Abstract: 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
College: College of Science
Issue: 12
Start Page: 023
End Page: 023