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

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${}^{\prime }$ 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 Poincaré 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.

V2: Added comment and reference

References in corpus (4)

• 6d Conformal Matter
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories

Cited by in corpus (6)

• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Higgs branch RG-flows via Decay and Fission
• The Higgs branch of Heterotic ALE instantons
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• Atomic Higgsings of 6D SCFTs II: Induced Flows