Perturbative tests of non-perturbative counting

TL;DR

This paper demonstrates that certain quarter-BPS dyons in N=4 theories exhibit nonperturbative behavior in one frame and perturbative in another, confirming the consistency of nonperturbative partition functions across duality frames.

Contribution

It provides a perturbative test of nonperturbative dyon counting formulas for states with nontrivial arithmetic invariants in N=4 theories.

Findings

Nonperturbative counting matches perturbative results for all invariant values.

Vanishing indexed degeneracy for these dyons across the moduli space.

Supports the validity of the nonperturbative partition functions.

Abstract

We observe that a class of quarter-BPS dyons in N=4 theories with charge vector (Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd (Q wedge P) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.