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

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