TL;DR
This paper investigates elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs, establishing a new constraint that enables bootstrapping these genera to higher degrees and deriving related physical quantities.
Contribution
It introduces a novel kinematical constraint on elliptic genera, allowing for their determination at higher degrees and conjecturing bounds on Gopakumar-Vafa invariants.
Findings
Derived the 6d Cardy formulas.
Obtained superconformal indices for (2,0) theories.
Conjectured vanishing bounds for refined Gopakumar-Vafa invariants.
Abstract
We study elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs from their modularity and explore the relation to topological string partition functions. We find a novel kinematical constraint that elliptic genera should follow, which determines elliptic genera at low base degrees and helps us to conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of related geometries. Using this, we can bootstrap the elliptic genera to arbitrary base degree, including D/E-type theories for which explicit formulas are only partially known. We utilize our results to obtain the 6d Cardy formulas and the superconformal indices for (2,0) theories.
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