N=8 Dyon Partition Function and Walls of Marginal Stability

TL;DR

This paper constructs an S-duality invariant partition function for 1/8 BPS dyons in type II string theory on T^6, accounting for walls of marginal stability where the dyon spectrum changes discontinuously.

Contribution

It extends previous work by explicitly incorporating walls of marginal stability into the dyon partition function, ensuring manifest S-duality invariance across different moduli space domains.

Findings

Partition function is S-duality invariant in all domains.

Spectrum jumps across walls match the wall crossing formula.

Partition function's poles encode spectrum discontinuities.

Abstract

We construct the partition function of 1/8 BPS dyons in type II string theory on T^6 from counting of microstates of a D1-D5 system in Taub-NUT space. Our analysis extends the earlier ones by Shih, Strominger and Yin and by Pioline by taking into account the walls of marginal stability on which a 1/8 BPS dyon can decay into a pair of half-BPS dyons. Across these walls the dyon spectrum changes discontinuously, and as a result the spectrum is not manifestly invariant under S-duality transformation of the charges. However the partition function is manifestly S-duality invariant and takes the same form in all domains of the moduli space separated by walls of marginal stability, -- the spectra in different domains being obtained by choosing different integration contours along which we carry out the Fourier transform of the partition function. The jump in the spectrum across a wall of marginal stability, calculated from the behaviour of the partition function at an appropriate pole, reproduces the expected wall crossing formula.