Index theorems and supersymmetry in the soliton sector

Imbimbo, Camillo ; Mukhi, Sunil (1984) Index theorems and supersymmetry in the soliton sector Nuclear Physics - Section B: Particle Physics, Field Theory and Statistical Systems, Physical Mathematics, 247 (2). pp. 471-483. ISSN 0550-3213

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/055032...

Related URL: http://dx.doi.org/10.1016/0550-3213(84)90559-5

Abstract

For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(h-) 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 = ½ supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments a la Witten are not able to exclude non-perturbative breaking.

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