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We compute the equivariant elliptic genera of several classes of ALE and ALFmanifolds using localization in gauged linear sigma models. In the sigma modelcomputation the equivariant action corresponds to chemical potentials for U(1)currents and the elliptic genera exhibit interesting pole structure as afunction of the chemical potentials. We use this to decompose the answers intopolar terms that exhibit wall crossing and universal terms. We compare ourresults to previous results on the large radius limit of the Taub-NUT ellipticgenus and also discuss applications of our results to counting of BPSworld-sheet spectrum of monopole strings in the 5d N=2 super Yang-Mills theoryand self-dual strings in the 6d N=(2,0) theories.

Elliptic genera of ALE and ALF manifolds from gauged linear sigma models