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
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.