Spectrum of CHL dyons from genus-two partition function

We compute the genus-two chiral partition function of the left-movingheterotic string for a $\mathbb{Z}_2$ CHL orbifold. The required twisteddeterminants can be evaluated explicitly in terms of the untwisted determinantsand theta functions using orbifold techniques. The dependence on Prym periodscancels neatly once summation over odd charges is properly taken into account.The resulting partition function is a Siegel modular form of level two andprecisely equals recently proposed dyon partition function for this model. Thisresult provides an independent weak coupling derivation of the dyon partitionfunction using the M-theory lift of string webs representing the dyons. Wediscuss generalization of this technique to general $\mathbb{Z}_N$ orbifolds.Comment: 25 pages, 2 figures, minor typos correcte