Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric Solitons

Abstract

We consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric $ϕ^4$ 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.