Energy, central charge, and the BPS bound for 1 + 1-dimensional supersymmetric solitons

We consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric θ4 and sine-Gordon models in 1 + 1 dimensions. In both models, we unambiguously calculate the correction to the energy in a simple renormalization scheme and obtain ΔH = -m/2π, in agreement with previous results. Furthermore, we show that there is an identical correction to the central charge, so that the BPS bound remains saturated in the one-loop approximation. We extend these results to arbitrary 1 + 1-dimensional supersymmetric theories