Sungjay Lee (Univ Chicago)
In the first part of this talk, we discuss the equivariant elliptic genera of ALE and ALF manifolds. The elliptic genera exhibit interesting pole structure as a function of the chemical potentials. We use this to decompose the answers into polar terms that exhibit wall-crossing and universal terms. We also discuss applications of our results to counting of BPS world-sheet spectrum of self-dual strings in the 6d N=(2,0) theories. In the second part of the talk, we consider two-dimensional N = (4, 4) supersymmetric gauge theories which do not have classical Higgs branches. These theories however are believed to have isolated quantum Higgs vacua with a mass gap. We provide a field theoretic argument for the existence of such vacua.