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 (21)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• D--branes and Spinning Black Holes
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Counting Dyons in N=4 String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Notes on the K3 Surface and the Mathieu group M_24
• Quantum Foam and Topological Strings
• BPS States, String Duality, and Nodal Curves on K3
• Refined, Motivic, and Quantum
• Lectures on Quantum Black Holes
• Dyon Spectrum in CHL Models
• Supersymmetric Index from Black Hole Entropy
• Elliptic Genera and N=2 Superconformal Field Theory
• Black Hole Hair Removal
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
• Corrections to the statistical entropy of five dimensional black holes
• Recounting Dyons in N=4 String Theory
• Gauge theory, topological strings, and S-duality
• Do All BPS Black Hole Microstates Carry Zero Angular Momentum?
• Notes on the proof of the KKV conjecture

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