Finite Yang-Mills integrals

Apr, 1998
7 pages
Published in:
  • Phys.Lett.B 435 (1998) 350-355
e-Print:
Report number:
  • AEI-063

Citations per year

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Abstract:
We use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D=3, N>3 and D=4, N>2 and, lastly, D >= 5, N >= 2. We conclude that the D=3 and D=4 integrals exist in the large N limit, and therefore lead to a well-defined, new type of Eguchi-Kawai reduced gauge theory. For the supersymmetric case, we check, up to SU(5), recently proposed exact formulas for the D=4 and D=6 D-instanton integrals, including the explicit form of the normalization factor needed to interpret the integrals as the bulk contribution to the Witten index.
Note:
  • 7 pages, LaTeX, REVTEX Report-no: AEI-063
  • gauge field theory: SU(N)
  • any-dimensional
  • partition function
  • dimensional reduction
  • dimension: 0
  • supersymmetry
  • instanton
  • Witten index