Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two

TL;DR

This paper proposes a set of constraints on quarter BPS dyon partition functions in N=4 string theories, leading to new formulas for torsion two dyons and insights into wall crossing phenomena.

Contribution

It introduces a general framework for constraining dyon partition functions and applies it to unknown cases, proposing a novel partition function and wall crossing formula.

Findings

Proposed a candidate partition function for torsion two dyons in heterotic string theory.

Derived a new wall crossing formula for decay into non-primitive charge dyons.

Reproduces known gauge theory results in specific limits.

Abstract

We propose a general set of constraints on the partition function of quarter BPS dyons in any N=4 supersymmetric string theory by drawing insight from known examples, and study the consequences of this proposal. The main ingredients of our analysis are duality symmetries, wall crossing formula and black hole entropy. We use our analysis to constrain the dyon partition function for two hitherto unknown cases -- the partition function of dyons of torsion two (i.e. gcd(Q\wedge P)=2) in heterotic string theory on T^6 and the partition function of dyons carrying untwisted sector electric charge in Z_2 CHL model. With the help of these constraints we propose a candidate for the partition function of dyons of torsion two in heterotic string theory on T^6. This leads to a novel wall crossing formula for decay of quarter BPS dyons into half BPS dyons with non-primitive charge vectors. In an appropriate limit the proposed formula reproduces the known result for the spectrum of torsion two dyons in gauge theory.