Affine characters at negative level and elliptic genera of non-critical strings

TL;DR

This paper investigates the elliptic genera of non-critical strings in 6d superconformal theories using affine Lie algebra characters at negative levels, providing a new ansatz and explicit formulas.

Contribution

It introduces a novel ansatz for elliptic genera based on affine Lie algebra characters at negative levels, supported by evidence from F-theory compactifications.

Findings

Derived closed-form elliptic genera using the new ansatz

Validated the ansatz through consistency along Higgsing trees

Connected affine characters at negative levels to 6d string theories

Abstract

We study the elliptic genera of the non-critical strings of six dimensional superconformal field theories from the point of view of the strings' worldsheet theory. We formulate a general ansatz for these in terms of characters of the affine Lie algebra associated to the 6d gauge group at negative level, and provide ample evidence for the validity of this ansatz for 6d theories obtained via F-theory compactification on elliptically fibered Calabi-Yau manifolds over a Hirzebruch base. We obtain novel closed form results for many elliptic genera in terms of our ansatz, and show that our results specialize consistently when moving along Higgsing trees.