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

Citation
H. Nastase et al., Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons, NUCL PHYS B, 542(1-2), 1999, pp. 471-514
Citations number
48
Categorie Soggetti
Physics
Journal title
NUCLEAR PHYSICS B
ISSN journal
05503213 → ACNP
Volume
542
Issue
1-2
Year of publication
1999
Pages
471 - 514
Database
ISI
SICI code
0550-3213(19990308)542:1-2<471:TBCTBB>2.0.ZU;2-F
Abstract
We fix the long-standing ambiguity in the one-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 p rinciple that ought to hold generally in quantum field theories with a topo logical sector: for vanishing mass and other dimensionful constants, the va cuum 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 non-triv ial relation between the quantum soliton mass and the quantum BPS bound and find a resolution. For N = 2 supersymmetric theories, there are no one-loo p corrections to the soliton mass and to the central charge land also no am biguities) so that the BPS bound is always saturated. Beyond one-loop there are no ambiguities in any theory, which we explicitly check by a two-loop calculation in the sine-Gordon model. (C) 1999 Elsevier Science B.V.