Scheme dependence of instanton counting in ALE spaces

There have been two distinct schemes studied in the literature for instanton counting in Ap−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 Ap−1 ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations. [email protected] [email protected] [email protected]