The Witten index in superspace, two-dimensional superanomaly in Yang-Mills and gravitational background, and superspace Schwinger-Dewitt heat kernel method
We consider the Witten index in superspace and show that it is closely related to the superspace Schwinger-DeWitt heat kernel. By evaluating the Witten index for the two-dimensional superspace Yang-Mills and gravitational systems we obtain the two-dimensional superanomaly in an efficient way. Furthermore we show an effective way to treat the three-dimensional supersymmetric Yang-Mills system by the superspace Schwinger-DeWitt heat kernel method. As a consequence, the supersymmetric Chern-Simons term is obtained.The author would like to thank Z. Yehsoo for guidance and courangement. In addition, it is a pleasure to acknowledge valuable discussions with Professor A. Das. This work is supported by the Agnes M. and George Messersmith Fellowship and the Rush-Rhees Fellowship.