Excited-state energies and supersymmetric indices

Abstract

We study multi-soliton states in two-dimensional N=2 supersymmetric theories. We calculate their energy exactly as a function of mass and volume in the simplest integrable N=2 theory, the sine-Gordon model at a particular coupling. These energies are related to the expectation value $I=tr[\exp (in\pi F)\exp (-H/T)]$, where F is the fermion number. For n=1, this is Witten's index; for n an odd integer, we argue that $I$ is an index in the sense that it is independent of all D-term variations.

arXiv comment20 pages, 6 figures, amslatex. Revision adds appendix describing analogous calculation for a free Dirac fermion. To appear in Advances in Theoretical and Mathematical Physics

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