The Hodge-Elliptic Genus, Spinning BPS States, and Black Holes

作者：Kachru Shamit; Tripathy Arnav^*

来源：Communications in Mathematical Physics, 2017, 355(1): 245-259.

DOI：10.1007/s00220-017-2910-1

We perform a refined count of BPS states in the compactification of M-theory on , keeping track of the information provided by both the and angular momenta in the SO(4) little group. Mathematically, this four variable counting function may be expressed via the motivic Donaldson-Thomas counts of , simultaneously refining Katz, Klemm, and Pandharipande's motivic stable pairs counts on K3 and Oberdieck-Pandharipande's Gromov-Witten counts on . 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.

• 出版日期2017-10