Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras

2023/11/07 by Baptiste Filoche, Filoche, Baptiste, Stefan Hohenegger +3
Mathematics · Physics and Astronomy · #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #FOS: Physical sciences #Gauge theory #Geometry #High Energy Physics - Theory (hep-th) #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quiver #Vertex (graph theory)

paper · pdf · doi:10.48550/arxiv.2311.03858

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We consider Little String Theories (LSTs) that are engineered by N parallel M5-branes probing a transverse ℤ_M geometry. By exploiting a dual description in terms of F-theory compactified on a toric Calabi-Yau threefold X_N,M, we establish numerous symmetries that leave the BPS partition function Z_N,M invariant. They furthemore act in a non-perturbative fashion from the point of view of the low energy quiver gauge theory associated with the LST. We present different group theoretical organisations of these symmetries, thereby generalising the results of [arXiv:1811.03387] to the case of generic M ≥ 1. We also provide a Mathematica package that allows to represent them in terms of matrices that act linearly on the Kähler parameters of X_N,M. From the perspective of dual realisations of the LSTs the symmetries found here act in highly nontrivial ways: as an example, we consider a formulation of Z_N,M in terms of correlation functions of a vertex operator algebra, whose commutation relations are governed by an affine quiver algebra. We show the impact of the symmetry transformations on the latter and discuss invariance of Z_N,M from this perspective for concrete examples.

Citations

• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• New theories in six dimensions and matrix description of M-theory on T5 and
• Connecting moduli spaces of Calabi-Yau threefolds
• The moduli space of 3-folds withK=0 may nevertheless be irreducible
• Consistency conditions for branes at orbifold singularities
• The web of Calabi-Yau hypersurfaces in toric varieties
• Point-like instantons on K3 orbifolds
• Rolling among Calabi-Yau vacua
• M‐strings, elliptic genera and N = 4 string amplitudes
• Branes at orbifolds versus Hanany Witten in six dimensions
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Worldsheet realization of the refined topological string
• D-branes, Quivers, and ALE Instantons
• F-theory and the classification of little strings

Related

• Symmetries in A-Type Little String Theories, Part I
• Branes, Quivers and BPS Algebras
• Dual Little Strings from F-Theory and Flop Transitions
• Surface Defects in A-type Little String Theories
• Quiver symmetries and wall-crossing invariance