Examples of M5-Brane Elliptic Genera
Davide Gaiotto, Xi Yin
TL;DR
This paper computes the modified elliptic genus of M5-branes on Calabi-Yau spaces using modular invariance and Gopakumar-Vafa invariants, revealing new relations among these invariants across degrees and genera.
Contribution
It introduces a method to determine elliptic genera of M5-branes on Calabi-Yau spaces and uncovers novel relations among Gopakumar-Vafa invariants.
Findings
Derived explicit elliptic genera for specific Calabi-Yau spaces.
Discovered nontrivial relations among Gopakumar-Vafa invariants.
Highlighted the role of modular invariance in string theory computations.
Abstract
We determine the modified elliptic genus of an M5-brane wrapped on various one modulus Calabi-Yau spaces, using modular invariance together with some known Gopakumar-Vafa invariants of small degrees. As a bonus, we find nontrivial relations among Gopakumar-Vafa invariants of different degrees and genera from modular invariance.
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