Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift

TL;DR

This paper computes exact degeneracies of BPS dyons and black holes in CHL orbifolds using Borcherds lift, revealing connections to M-theory and heterotic string theory.

Contribution

It introduces a novel application of Borcherds lift to compute dyon and black hole degeneracies in CHL models, linking mathematical and physical frameworks.

Findings

Exact formulas for dyon degeneracies in CHL orbifolds

Physical interpretation of the Hodge anomaly as a Kaluza-Klein 6-brane contribution

Two-loop heterotic string partition function consistent with M-theory picture

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.