Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality

TL;DR

This paper revisits heterotic little string theories on ALE spaces, focusing on non-trivial flat connections, and explores their 2-group symmetries, T-duality constraints, and 6d quiver constructions.

Contribution

It extends previous work by analyzing non-trivial flat connections and their 2-group symmetries in heterotic LSTs on ALE spaces using 6d conformal matter.

Findings

Identification of higher-one form symmetries forming 2-groups with 0-form symmetries.

Matching of R-symmetry 2-group structure constants as T-duality constraints.

Construction of these theories as generalized 6d quivers.

Abstract

In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic $E_8 \times E_8$ five-branes probing ALE singularities, building on and extending previous results on the subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus are the cases corresponding to choices of non-trivial flat connections at infinity. The latter are in particular interesting for the exceptional ALE singularities, where a brane realization in Type I$'$ is lacking. Our approach to determine these models is based on 6d conformal matter: we determine these theories as generalized 6d quivers. All these LSTs have a higher-one form symmetry which forms a 2-group with the zero-form Poincar\'e symmetry, the R-symmetry and the other global symmetries: the matching of the R-symmetry two-group structure constant is a stringent constraint for T-dualities, which we use in combination with the matching of 5d Coulomb branches and flavor symmetries upon circle reduction, as a consistency check for the realization of the 6d LSTs we propose.