Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-05-16
Annals Phys. 308 (2003) 78-114
Physics
High Energy Physics
High Energy Physics - Theory
36 pages
Scientific paper
10.1016/S0003-4916(03)00133-7
A fully quantum version of the Witten-Olive analysis of the central charge in the N=1 Wess-Zumino model in $d=2$ with a kink solution is presented by using path integrals in superspace. We regulate the Jacobians with heat kernels in superspace, and obtain all superconformal anomalies as one Jacobian factor. The conserved quantum currents differ from the Noether currents by terms proportional to field equations, and these terms contribute to the anomalies. We identify the particular variation of the superfield which produces the central charge current and its anomaly; it is the variation of the auxiliary field. The quantum supersymmetry algebra which includes the contributions of superconformal anomalies is derived by using the Bjorken-Johnson-Low method instead of semi-classical Dirac brackets. We confirm earlier results that the BPS bound remains saturated at the quantum level due to equal anomalies in the energy and central charge.
Fujikawa Kazuo
van Nieuwenhuizen Peter
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