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

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

1998-02-11

arxiv.org/abs/hep-th/9802074v1

Nucl.Phys. B542 (1999) 471-514

Physics

High Energy Physics

High Energy Physics - Theory

38 pages

Scientific paper

10.1016/S0550-3213(98)00773-1

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.

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