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

TL;DR

This paper calculates one-loop quantum corrections to soliton energies and central charges in 1+1 dimensional supersymmetric models, confirming the BPS bound remains saturated at this order.

Contribution

It provides an unambiguous calculation of quantum corrections to soliton energies and central charges, extending results to general 1+1D supersymmetric theories.

Findings

Quantum correction to energy: ΔH = - m/(2π)

Identical correction to central charge

BPS bound remains saturated at one-loop

Abstract

We consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric $\phi^4$ 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 $\Delta H = - m/(2\pi)$, 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.