Tao Probing the End of the World

TL;DR

This paper presents a novel 5-brane web description of the E-string theory, linking M-theory configurations with topological string calculations to derive the E-string elliptic genus generating function.

Contribution

It introduces a new type IIB 5-brane web framework for the E-string theory, facilitating combinatorial computation of its elliptic genera via topological vertex methods.

Findings

Derived a combinatorial formula for the E-string elliptic genus

Connected 5-brane web configurations with topological string partition functions

Enabled calculation of the full partition function on local 1/2 K3 surface

Abstract

We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1/2 K3 surface.