AbstractTheory of quantum multiplication and Gromov-Witten invariants of a smoothprojective algebraic variety X deals with enumerative questions concerningcurves in X. A long time ago physicists E. Witten, R. Dijkgraaf, E. Verlinde, andH. Verlinde discovered a remarkable system of non-linear differential equations on the generating series for Gromov-Witten invariants. In particular, onecan calc...
AbstractIn this talk, I will identify degeneracies in the energy spectra of quantum theories that occur at integer values of the continuous parameter N of an analytically continued global O(N) symmetry. I will first present a few examples in the critical O(N) CFT at the Wilson-Fisher fixed point (d=4-epsilon) at the first order of epsilon-expansion. Then I will argue the degeneracies happen for...