Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons

TL;DR

This paper resolves longstanding ambiguities in the quantum mass of supersymmetric solitons by using symmetry-based boundary conditions and a physical principle relating vacuum energies, with detailed analysis in 1+1D models including sine-Gordon.

Contribution

It introduces a boundary condition approach based on symmetries and topology to fix quantum mass ambiguities in supersymmetric solitons, and clarifies the relation to the BPS bound.

Findings

One-loop corrections are fixed by the new boundary conditions.

In N=2 theories, no one-loop corrections or ambiguities exist.

Two-loop calculations confirm the absence of ambiguities.

Abstract

We fix the long-standing ambiguity in the 1-loop contribution to the mass of a 1+1-dimensional supersymmetric soliton by adopting a set of boundary conditions which follow from the symmetries of the action and which depend only on the topology of the sector considered, and by invoking a physical principle that ought to hold generally in quantum field theories with a topological sector: for vanishing mass and other dimensionful constants, the vacuum energies in the trivial and topological sectors have to become equal. In the two-dimensional N=1 supersymmetric case we find a result which for the supersymmetric sine-Gordon model agrees with the known exact solution of the S-matrix but seems to violate the BPS bound. We analyze the nontrivial relation between the quantum soliton mass and the quantum BPS bound and find a resolution. For N=2 supersymmetric theories, there are no one-loop corrections to the soliton mass and to the central charge (and also no ambiguities) so that the BPS bound is always saturated. Beyond 1-loop there are no ambiguities in any theory, which we explicitly check by a 2-loop calculation in the sine-Gordon model.