BPS Quivers and Spectra of Complete N=2 Quantum Field Theories

Abstract

We study the BPS spectra of N=2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.

55 pages, 32 Figures; corrected typos, added references; changed sign convention for drawing arrows in quiver (i.e. Section 2.2) for consistency

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Cited by in corpus (53)

• Four-Dimensional SCFTs from M5-Branes
• Spectral networks
• On the Superconformal Index of Argyres-Douglas Theories
• N=2 Quantum Field Theories and Their BPS Quivers
• More on the N=2 superconformal systems of type $D_p(G)$
• Surface Defects and Chiral Algebras
• Infinitely many N=2 SCFT with ADE flavor symmetry
• Braids, Walls, and Mirrors
• Stability conditions and quantum dilogarithm identities for Dynkin quivers
• The representation type of Jacobian algebras
• Categorical Tinkertoys for N=2 Gauge Theories
• Cluster categories for marked surfaces: punctured case
• Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions
• An Index Formula for Supersymmetric Quantum Mechanics
• Quantum Higgs branches of isolated N=2 superconformal field theories
• W_3 irregular states and isolated N=2 superconformal field theories
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• New Directions in Bipartite Field Theories
• More Arnold's N = 2 superconformal gauge theories
• Toda Theory From Six Dimensions
• Line defects and (framed) BPS quivers
• Half--Hypers and Quivers
• BPS spectrum of Argyres-Douglas theory via spectral network
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• Spectral Networks and Snakes
• Network, Cluster coordinates and N=2 theory I
• Geometric engineering of (framed) BPS states
• Kinetic Mixing at Strong Coupling
• Donaldson-Thomas trasnsformations of moduli spaces of G-local systems
• Network, cluster coordinates and N = 2 theory II: Irregular singularity
• Dessins d'Enfants in $\mathcal{N}=2$ Generalised Quiver Theories
• The quiver approach to the BPS spectrum of a 4d N=2 gauge theory
• BPS spectrum, wall crossing and quantum dilogarithm identity
• The BPS Spectrum Generator In 2d-4d Systems
• Regge Trajectories in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Superconformal Index, BPS Monodromy and Chiral Algebras
• Counting Trees in Supersymmetric Quantum Mechanics
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Weak Coupling Chambers in N=2 BPS Quiver Theory
• Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
• $Y$ systems, $Q$ systems, and 4D $\mathcal{N}=2$ supersymmetric QFT
• Equivalence of Three Wall Crossing Formulae
• About the Absence of Exotics and the Coulomb Branch Formula
• FQHE and $t{t}^{\ast }$ geometry
• Four-dimensional N=2 Field Theory and Physical Mathematics
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• Algebraicity and Asymptotics: An explosion of BPS indices from algebraic generating series
• Attractor invariants, brane tilings and crystals
• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies
• Quiver Gauge theories from Lie Superalgebras
• Mutation, Witten Index, and Quiver Invariant
• BPS spectra from BPS graphs
• Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review