Aspects of Gauge Theory on Commutative and Noncommutative Tori

Details Aspects of Gauge Theory on Commutative and Noncommutative Tori Aspects of Gauge Theory on Commutative and Noncommutative Tori

2001-03-20

arxiv.org/abs/hep-th/0103168v3

JHEP 0105:022,2001

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 3 figures, latex, references added, minor corrections

Scientific paper

10.1088/1126-6708/2001/05/022

We study aspects of gauge theory on tori which are a consequences of Morita equivalence. In particular we study the behavior of gauge theory on noncommutative tori for arbitrarily close rational values of Theta. For such values of Theta, there are Morita equivalent descriptions in terms of Yang-Mills theories on commutative tori with very different magnetic fluxes and rank. In order for the correlators of open Wilson lines to depend smoothly on Theta, the correlators of closed Wilson lines in the commutative Yang-Mills theory must satisfy strong constraints. If exactly satisfied, these constraints give relations between small and large N gauge theories. We verify that these constraints are obeyed at leading order in the 1/N expansion of pure 2-d QCD and of strongly coupled N=4 super Yang-Mills theory.

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