Five-Brane Webs and Highest Weight Representations

Abstract

We consider BPS-counting functions ${\mathcal{Z}}_{N,M}$ of $N$ parallel M5-branes probing a transverse ${\mathbb{Z}}_M$ orbifold geometry. These brane web configurations can be dualised into a class of toric non-compact Calabi-Yau threefolds which have the structure of an elliptic fibration over (affine) $A_{N-1}$. We make this symmetry of ${\mathcal{Z}}_{N,M}$ manifest in particular regions of the parameter space of the setup: we argue that for specific choices of the deformation parameters, the supercharges of the system acquire particular holonomy charges which lead to infinitely many cancellations among states contributing to the partition function. The resulting (simplified) ${\mathcal{Z}}_{N,M}$ can be written as a sum over weights forming a single irreducible representation of the Lie algebra ${\mathfrak{a}}_{N-1}$ (or its affine counterpart). We show this behaviour explicitly for an extensive list of examples for specific values of $(N,M)$ and generalise the arising pattern for generic configurations. Finally, for a particular compact M5-brane setup we use this form of the partition function to make the duality $N\leftrightarrow M$ manifest.

70 pages

References in corpus (43)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Evidence for F-Theory
• The Topological Vertex
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• The Refined Topological Vertex
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Some Comments On String Dynamics
• Integrating Over Higgs Branches
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• A brief review of "little string theories"
• Five-branes And $M$-Theory On An Orbifold
• Branes and Six Dimensional Supersymmetric Theories
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• M-Strings
• Non-abelian Tensor-multiplet Anomalies
• Matrix Models, Geometric Engineering and Elliptic Genera
• Point-like Instantons on K3 Orbifolds
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, N=(2,0) Field Theories
• On orbifolds of M-Strings
• Strings of Minimal 6d SCFTs
• F-theory and the Classification of Little Strings
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• F-Theory, Spinning Black Holes and Multi-string Branches
• Mirror Symmetries for Brane Configurations and Branes at Singularities
• The Large N Limit of the (2,0) Superconformal Field Theory
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• M String, Monopole String and Modular Forms
• Equations of the (2,0) Theory and Knitted Fivebranes
• Dual Little Strings from F-Theory and Flop Transitions
• Self-Duality and Self-Similarity of Little String Orbifolds
• Refined geometric transition and $qq$-characters
• From strings in 6d to strings in 5d
• Bound States of Little Strings and Symmetric Orbifold CFTs
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Arithmetic and Hyperbolic Structures in String Theory
• Surface Operators from M-strings
• M-strings and Transverse Orbifold

Cited by in corpus (9)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• Revisiting the classifications of 6d SCFTs and LSTs
• Triality in Little String Theories
• Dual Little Strings and their Partition Functions
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Symmetries in A-Type Little String Theories, Part I
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras