An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings

TL;DR

This paper constructs an elliptic refined topological vertex for the elliptic Ding-Iohara-Miki algebra, demonstrating its ability to reproduce the elliptic genus of M-strings and establishing it as an algebra intertwiner.

Contribution

It introduces an elliptic version of the refined topological vertex and links it to the elliptic Ding-Iohara-Miki algebra, providing new tools for studying M-strings.

Findings

The elliptic vertex reproduces the elliptic genus of M-strings.

The vertex acts as an intertwiner of the elliptic Ding-Iohara-Miki algebra.

Explicit construction of the elliptic vertex and its algebraic properties.

Abstract

We write down a vertical representation for the elliptic Ding-Iohara-Miki algebra, and construct an elliptic version of the refined topological vertex of Awata, Feigin and Shiraishi. We show explicitly that this vertex reproduces the elliptic genus of M-strings, and that it is an intertwiner of the algebra.