Scheme dependence of instanton counting in ALE spaces

Understand

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.