Supersymmetry on Curved Space and Localization: An Example on S3
Abstract: We present a basic introduction to the Super Poincaré algebra in 4D, then constructthe N = 1 Super Yang-Mills in 4D. By analogue we expand to the case of N = 1 Super Yang-Mills in 10D. Then by a method of dimensional reduction we getcertain supersymmetric theories in d <= 7 and restrict to spherical backgrounds. Wethen introduce a localization argument by ways of a cohomology on the configuration space of our theory. Finally we apply both techniques to acquire N = 2 Super Yang-Mills on S3, adding the Chern-Simons term and computing the exact partitionfunction, additionally giving an example for the case of U(N) gauge theories.
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