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

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 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 non-trivial 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 land also no ambiguities) 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.