The Hodge-elliptic genus, spinning BPS states, and black holes

Abstract

We perform a refined count of BPS states in the compactification of M-theory on $K3\times T^2$, keeping track of the information provided by both the $SU(2{)}_L$ and $SU(2{)}_R$ angular momenta in the $SO(4)$ little group. Mathematically, this four variable counting function may be expressed via the motivic Donaldson-Thomas counts of $K3\times T^2$, simultaneously refining Katz, Klemm, and Pandharipande's motivic Donaldson-Thomas counts on $K3$ and Oberdieck-Pandharipande's Gromov-Witten counts on $K3\times T^2$. This provides the first full answer for motivic curve counts of a compact Calabi-Yau threefold. Along the way, we develop a Hodge-elliptic genus for Calabi-Yau manifolds -- a new counting function for BPS states that interpolates between the Hodge polynomial and the elliptic genus of a Calabi-Yau.

21 pages. Comments welcome!

References in corpus (4)

• Notes on the K3 Surface and the Mathieu group M_24
• Lectures on Quantum Black Holes
• Supersymmetric Index from Black Hole Entropy
• Corrections to the statistical entropy of five dimensional black holes

Cited by in corpus (8)

• On the BPS sector in AdS_3/CFT_2 Holography
• The Holographic Landscape of Symmetric Product Orbifolds
• Hodge-elliptic genera and how they govern K3 theories
• Fortuity and Supergravity
• Symmetries of the refined D1/D5 BPS spectrum
• BPS jumping loci are automorphic
• Calabi-Yau manifolds and sporadic groups
• Elliptic genus of singular algebraic varieties and quotients