Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-03-27
J.Math.Phys. 47 (2006) 012303
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, no figures, Appendices B and C are added, changes in the text, references are added
Scientific paper
10.1063/1.2162127
We investigate cohomological gauge theories in noncommutative R^{2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R^{2D} and a partition function of a cohomological field theory in R^{2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the N=4 U(1) gauge theory in noncommutative R^4, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.
Sako Akifumi
Suzuki Toshiya
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