Scheme dependence of instanton counting in ALE spaces

Abstract

There have been two distinct schemes studied in the literature for instanton counting in A_(p−1) asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes — namely the counting of orbifolded instantons and instanton counting in the resolved space — lead in general to different results for partition functions. We illustrate this observation in the case of N=2 U(N) gauge theory with 2N flavors on the A_(p−1) ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations.

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