N=8 Dyon Partition Function and Walls of Marginal Stability
arXiv:0803.1014 · doi:10.1088/1126-6708/2008/07/118
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.
LaTeX file, 22 pages; v3: minor clarifications added; v4: minor expansion; v5: minor corrections
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