Bootstrapping ADE M-strings

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.

Automated summary

By studying the elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs and exploring their modularity, a novel kinematical constraint has been identified. This constraint helps determine elliptic genera at low base degrees and allows for conjecturing a vanishing bound for refined Gopakumar-Vafa invariants. By utilizing these results, the 6d Cardy formulas and superconformal indices for (2,0) theories have been obtained.