Symmetries in A-Type Little String Theories, Part II

TL;DR

This paper explores the symmetries and modular properties of A-type little string theories, providing explicit series expansions for N=2,3,4, and proposing functions that resum instanton sectors and unify gauge symmetry and modularity.

Contribution

It introduces a class of functions that resum instanton sectors in A-type little string theories and links them to modular forms and gauge symmetry, extending previous analyses.

Findings

Explicit series expansions for N=2,3,4 cases.

Identification of functions that resum instanton sectors.

Consistency checks confirming the proposed functions' validity.

Abstract

We continue our study of symmetries of a class of little string theories of A-type, which are engineered by $N$ parallel M5-branes probing a flat transverse space. Extending the analysis of the companion paper, we discuss the part of the free energy that is sensitive to the details of the $\mathfrak{a}_{N-1}$ gauge structure, by computing explicit series expansions for the cases $N=2,3,4$. Based on these examples, we find a class of functions that we conjecture to resum whole sectors in the instanton expansion of the free energy and which combine in a natural manner its modular properties as well as the gauge symmetry. These functions have previously been introduced in the literature as the generating functions of multi-divisor sums and in the case $N=2$ can also be cast into the form of a generalised Eisenstein series. We use these resummed contributions to the free energy to perform a number of non-trivial consistency checks for our results.