Excited-state energies and supersymmetric indices

Paul Fendley
1997 Advances in Theoretical and Mathematical Physics  
We study multi-soliton states in two-dimensional 7V=2 supersymmetric theories. We calculate their energy exactly as a function of mass and volume in the simplest integrable iV=2 supersymmetric theory, the sine-Gordon model at a particular coupling. These energies are related to the expectation value X = tr[exp(zn7rF) exp(-H/T)], where F is the fermion number. For n=l, this is Witten's index; for n an odd integer, we argue that X is an index in the sense that it is independent of all D-term variations.
doi:10.4310/atmp.1997.v1.n2.a2 fatcat:locc3y7w2ndsxbwtmyvhqa7pa4