No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons

Abstract

We determine the generating functions of 1/4 BPS dyons in a class of 4d $\mathcal{N}=4$ string vacua arising as CHL orbifolds of $K3\times T^2$, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be described as multiplicative lifts of certain supersymmetric indices (twining genera) on the worldsheet of the corresponding nonlinear sigma model on K3. As a consequence, our procedure also leads to an explicit derivation of almost all of these twining genera. The worldsheet indices singled out in this way match precisely a set of functions of interest in moonshine, as predicted by a recent conjecture.

55 + 22 pages

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Cited by in corpus (14)

• The Holographic Landscape of Symmetric Product Orbifolds
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Siegel Paramodular Forms and Sparseness in AdS${}_3$/CFT${}_2$
• Dyon degeneracies from Mathieu moonshine
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• On Mathieu moonshine and Gromov-Witten invariants
• Symmetries of the refined D1/D5 BPS spectrum
• Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N}=4$ CHL models
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• Calabi-Yau manifolds and sporadic groups
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Some comments on symmetric orbifolds of K3
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results