Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6

TL;DR

This paper generalizes the dyon partition function in heterotic string theory on T^6 to include dyons of arbitrary torsion, ensuring consistency with duality, wall crossing, and black hole entropy constraints.

Contribution

It introduces a new formula for dyon partition functions of any torsion, extending the original torsion 1 case and satisfying multiple theoretical constraints.

Findings

Proposed a generalized partition function for dyons of arbitrary torsion.

Derived a universal wall crossing formula valid for non-primitive decay products.

Confirmed consistency with S-duality, entropy, and gauge theory limits.

Abstract

The original proposal of Dijkgraaf, Verlinde and Verlinde for the quarter BPS dyon partition function in heterotic string theory on T^6 is known to correctly produce the degeneracy of dyons of torsion 1, i.e. dyons for which gcd(Q\wedge P)=1. We propose a generalization of this formula for dyons of arbitrary torsion. Our proposal satisfies the constraints coming from S-duality invariance, wall crossing formula, black hole entropy and the gauge theory limit. Furthermore using our proposal we derive a general wall crossing formula that is valid even when both the decay products are non-primitive half-BPS dyons.