Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry

TL;DR

This paper investigates quantum corrections to soliton masses in two-dimensional supersymmetric models, revealing an anomaly in the central charge that preserves BPS saturation at all orders.

Contribution

It demonstrates that BPS saturation remains valid quantum mechanically and uncovers an anomalous correction to the classical central charge in N=1 supersymmetric theories.

Findings

BPS saturation holds at quantum level in all orders.

Anomalous term modifies the classical central charge.

One-loop calculations confirm the anomaly.

Abstract

We reexamine the issue of the soliton mass in two-dimensional models with N =1 supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion. Our key finding is an anomaly in the expression for the central charge. The classical central charge, equal to the jump of the superpotential, is amended by an anomalous term proportional to the second derivative of the superpotential. The anomaly is established by various methods in explicit one-loop calculations. We argue that this one-loop result is not affected by higher orders. We discuss in detail how the impact of the boundary conditions can be untangled from the soliton mass calculation. In particular, the soliton profile and the energy distribution are found at one loop. A "supersymmetry" in the soliton mass calculations in the non-supersymmetric models is observed.