Non commutative geometry and super Yang-Mills theory

Details Non commutative geometry and super Yang-Mills theory Non commutative geometry and super Yang-Mills theory

1998-04-17

arxiv.org/abs/hep-th/9804120v2

Phys.Lett. B451 (1999) 324-335

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX, two .gif files of (hand sketched) figures; a misprint corrected and some references added

Scientific paper

10.1016/S0370-2693(99)00214-2

We aim to connect the non commutative geometry ``quotient space'' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size \Sigma / N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification.

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