Abstract

In 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 general theories with O(N) symmetry by analytically continuing the character of irreducible representation (irrep) of O(N) and then matching the partition function at integer values of N. We give a specialization rule of the character of continued irreps of O(N) for every integer N. The degeneracies are enforced by the requirement that evanescent states, carrying different irreps of the analytic continuation of O(N), fall out of the spectrum in the partition function via pair annihilation. Therefore the degeneracies also hold non-perturbatively.