Elliptic Genus of E-strings

TL;DR

This paper computes the elliptic genus of 2d N=(0,4) gauge theories describing E-strings, confirming known results and providing explicit calculations for multiple E-strings, linking to topological string theory and instanton calculus.

Contribution

It introduces a method to compute the elliptic genus for arbitrary numbers of E-strings and connects these results with topological string theory and 5d gauge theory.

Findings

Agreement with known single and two E-string results

Explicit computations for low numbers of E-strings

Provides all genus partition function of refined topological strings on a specific Calabi-Yau

Abstract

We study a family of 2d N=(0,4) gauge theories which describes at low energy the dynamics of E-strings, the M2-branes suspended between a pair of M5 and M9 branes. The gauge theory is engineered using a duality with type IIA theory, leading to the D2-branes suspended between an NS5-brane and 8 D8-branes on an O8-plane. We compute the elliptic genus of this family of theories, and find agreement with the known results for single and two E-strings. The partition function can in principle be computed for arbitrary number of E-strings, and we compute them explicitly for low numbers. We test our predictions against the partially known results from topological strings, as well as from the instanton calculus of 5d Sp(1) gauge theory. Given the relation to topological strings, our computation provides the all genus partition function of the refined topological strings on the canonical bundle over 1/2 K3.