Noncommutative geometry and superYang-Mills theory
Apr, 1998Citations per year
Abstract:
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.Note:
- 11 pages, LaTeX, two .gif files of (hand sketched) figures; a misprint corrected and some references added Report-no: SU
- geometry: noncommutative
- gauge field theory: U(N)
- supersymmetry
- torus
- M-theory
- coupling constant: scaling
- expansion 1/N
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