Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
Atish Dabholkar, Suresh Nampuri
TL;DR
The paper presents an exact counting framework for dyon degeneracies and spinning black holes in CHL compactifications by constructing Siegel modular forms of level $N$ via a generalized Borcherds (multiplicative) lift from weak Jacobi seeds of weight $0$ and index $1$. It provides a concrete realization for $(N,k)=(2,6)$, obtaining the seed and product representation for $\Phi_6$, and embeds the construction in a physical 4d–5d lift where the exponential and Hodge anomaly encode symmetric-product degeneracies of the D1-D5-P system and KK5 momentum bound states, respectively. The multiplicative lift yields a natural genus-two interpretation: the Siegel form acts as a two-loop partition function of the left-moving heterotic string, consistent with a string-web/M-theory picture of dyons. Altogether, the work ties dyon counting in CHL orbifolds to Borcherds algebras and genus-two string dynamics, suggesting deep underlying symmetries in string theory.
Abstract
The degeneracies of supersymmetric quarter BPS dyons in four dimensions and of spinning black holes in five dimensions in a CHL compactification are computed exactly using Borcherds lift. The Hodge anomaly in the construction has a physical interpretation as the contribution of a single M-theory Kaluza-Klein 6-brane in the 4d-5d lift. Using factorization, it is shown that the resulting formula has a natural interpretation as a two-loop partition function of left-moving heterotic string, consistent with the heuristic picture of dyons in the M-theory lift of string webs.