N=8 Dyon Partition Function and Walls of Marginal Stability

TL;DR

This work constructs a manifestly S-duality invariant partition function for 1/8 BPS dyons in type IIB string theory on $T^6$ by counting D1-D5 microstates in Taub-NUT space and encodes moduli-space dependence via contour choices in a Fourier transform. It shows that across walls of marginal stability the spectrum jumps in a controlled way captured by residues at poles of a single analytic function, reproducing the expected wall-crossing behavior. Extending previous ${\cal N}=4$ analyses to ${\cal N}=8$, the study demonstrates a universal partition function that remains valid across all moduli-space domains and clarifies the pivotal role of the $k=0$ sector for duality invariance. The results provide a consistent, duality-respecting framework for counting 1/8 BPS dyons in ${\cal N}=8$ theories and illuminate the parallel structure of wall crossing with lower-supersymmetry cases.

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.