Index theorems and supersymmetry in the soliton sector
Abstract
For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(ħ) correction to the soliton mass. At the same order the Bogomolny bound is shown, by an explicit computation, to be saturated. The non-vanishing of the mass correction is traced to the existence of supersymmetry violating surface terms in the soliton lagrangian, while the saturation of the Bogomolny bound is a consequence of the absence of spontaneous breaking of N = {1}/{2} supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments à la Witten are not able to exclude non-perturbative breaking.
- Publication:
-
Nuclear Physics B
- Pub Date:
- December 1984
- DOI:
- 10.1016/0550-3213(84)90559-5
- Bibcode:
- 1984NuPhB.247..471I