Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the Z2 model

Motivated by recent advances in Donaldson-Thomas theory, four-dimensional N = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of untwisted quarter-BPS dyons in the heterotic Z(2) CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) subset of Sp(4)(Z) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 x T-2)/Z(2), as suggested by string duality with type IIA theory on X.

Automated summary

This study examines the four-dimensional N = 4 string-string duality in a reduced rank theory on a less studied BPS sector, focusing on the heterotic Z(2) CHL model. By identifying candidate partition functions for untwisted quarter-BPS dyons in this model, the study reveals meromorphic Siegel modular forms that generate BPS indices for dyons with untwisted sector electric charge. The new partition functions are shown to satisfy expected constraints from wall-crossing, S-duality symmetry, and black hole entropy based on the Gauss-Bonnet term in the effective action.