The Casimir effect for susy solitons

TL;DR

This paper explores the quantum corrections to the mass and central charge of supersymmetric solitons, revealing how regularization, anomalies, and field winding influence these corrections in low-dimensional theories.

Contribution

It provides new insights into the nonvanishing quantum corrections to susy solitons, emphasizing the roles of regularization, anomalies, and boundary conditions.

Findings

Quantum corrections to mass and central charge are nonzero despite boson-fermion cancellation.

An anomaly in the central charge is essential for saturating the Bogomolnyi bound.

Winding of classical fields affects quantum field behavior at large distances.

Abstract

We discuss new insights into the quantum physics of solitons developed since 1997: why quantum corrections to the mass M and the central charge Z of solitons in supersymmetric (susy) field theories in 1+1 and 2+1 dimensions are nonvanishing, despite the fact that the zero-point energies of bosons and fermions seem to cancel each other, and the central charge is an integral of a total space derivative which naively seems to get contributions only from regions far removed from the soliton. Crucial are: (1) the requirement that the regularization scheme not only makes calculations finite, but it also should preserve (ordinary) supersymmetry, (2) the renormalization condition that tadpoles vanish in the trivial vacuum, (3) an anomaly in the central charge which is actually needed to saturate the Bogomolnyi bound, (4) the influence of the winding of classical fields on the quantum fields far away from the soliton.