2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150684We 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 $I= tr [\exp(inπF) \exp(-H/T)]$, 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.20 pages, 6 figures, amslatex. Revision adds appendix describing analogous calculation for a free Dirac fermion. To appear in Advances in Theoretical and Mathematical PhysicsHigh Energy Physics - Theorytext