Soliton masses in supersymmetric theories

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The semiclassical approximation, the familiar sum of frequencies, to the quantum- mechanical masses of solitons is ambiguous in theories with supersymmetric couplings: the approximation is unacceptably sensitive to the definition of the infinite-volume limit. The ambiguity can be resolved by means of a systematic mass-calculation procedure derived from the supersymmetry algebra. We apply this method to a large class of two- dimensional models, and find that in O(h{stroke}) the quantum-mechanical mass of a kink differs from its classical mass by a universal expression that has no dependence on the details of the interaction. The difference contains an ultraviolet divergence that exactly cancels the divergence in the classical mass. This contradicts recent claims that the difference must be zero. This result can also be checked using a number of other techniques but we argue that in spacetimes of dimension greater than two only the procedure derived from the supersymmetry algebra is likely to have any practical value. In two dimension the difference between the quantum and classical masses can be related to properties of the amplitudes with which elementary bosons and fermions are scattered by a kink-antikink pair. Contrary to naive expectations these amplitudes are not identical; they nevertheless satisfy a supersymmetry Ward identity. © 1979.




Schonfeld, J. F. (1979). Soliton masses in supersymmetric theories. Nuclear Physics, Section B, 161(1), 125–155.

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