Duality Cascades and Affine Weyl Groups
arXiv:2112.13616 · doi:10.1007/JHEP05(2022)132
Abstract
Brane configurations in a circle allow subsequent applications of the Hanany-Witten transitions, which are known as duality cascades. By studying the process of duality cascades corresponding to quantum curves with symmetries of Weyl groups, we find a hidden structure of affine Weyl groups. Namely, the fundamental domain of duality cascades consisting of all the final destinations is characterized by the affine Weyl chamber and the duality cascades are realized as translations of the affine Weyl group, where the overall rank in the brane configuration associates to the grading operator of the affine algebra. The structure of the affine Weyl group guarantees the finiteness of the processes and the uniqueness of the endpoint of the duality cascades. In addition to the original duality cascades, we can generalize to the cases with Fayet-Iliopoulos parameters. There we can utilize the Weyl group to analyze the fundamental domain similarly and find that the fundamental domain continues to be the affine Weyl chamber. We further interpret the Weyl group we impose as a "half" of the Hanany-Witten transition.
arXiv comment51 pages, 12 eps figures; v3: published version
References in corpus (60)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Supergravity and a Confining Gauge Theory: Duality Cascades and SB-Resolution of Naked Singularities
- Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
- Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
- Fractional M2-branes
- From weak to strong coupling in ABJM theory
- Giant Gravitons in Conformal Field Theory
- Entropy of Near-Extremal Black p-branes
- N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
- Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
- ABJM theory as a Fermi gas
- A Geometric Unification of Dualities
- Non-perturbative effects and the refined topological string
- Nonperturbative aspects of ABJM theory
- Exact Results in ABJM Theory from Topological Strings
- A supermatrix model for N=6 super Chern-Simons-matter theory
- Summing Up All Genus Free Energy of ABJM Matrix Model
- On the moduli space of elliptic Maxwell-Chern-Simons theories
- Quantum Geometry of Refined Topological Strings
- Instanton Effects in ABJM Theory from Fermi Gas Approach
- Refined stable pair invariants for E-, M- and [p,q]-strings
- Instanton Bound States in ABJM Theory
- Membrane instantons from a semiclassical TBA
- Exact Results on the ABJM Fermi Gas
- D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
- Geometric Aspects of Painlevé Equations
- Matrix models from operators and topological strings, 2
- Matrix models from operators and topological strings
- Direct derivation of "mirror" ABJ partition function
- Exact ABJM Partition Function from TBA
- ABJ Fractional Brane from ABJM Wilson Loop
- ABJM Wilson Loops in Arbitrary Representations
- Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
- Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
- Instanton Effects in Orbifold ABJM Theory
- Instanton Effects in Orientifold ABJM Theory
- Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
- Exact relations between M2-brane theories with and without Orientifolds
- Large N behavior of mass deformed ABJM theory
- Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
- Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
- Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
- ABJM Membrane Instanton from Pole Cancellation Mechanism
- ABJM Theory with mass and FI deformations and Quantum Phase Transitions
- Superconformal Chern-Simons Theories from del Pezzo Geometries
- Duality cascades and duality walls
- Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
- Dualities in ABJM Matrix Model from Closed String Viewpoint
- Spectral Theories and Topological Strings on del Pezzo Geometries
- Giambelli Identity in Super Chern-Simons Matrix Model
- Large N non-perturbative effects in superconformal Chern-Simons theories
- Hanany-Witten Transition in Quantum Curves
- Two-Point Functions in ABJM Matrix Model
- ABJM Matrix Model and 2D Toda Lattice Hierarchy
- Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
- Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
- Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
- Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
- Brane Transitions from Exceptional Groups
- 3d dualities with decoupled sectors and brane transitions