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

2011/09/22 by Murad Alim, Sergio Cecotti, Alim, Murad +9 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1109.4941

openalex publication_date 2011/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quivers with potentials associated to triangulated surfaces, Part II: Arc representations
• Cluster algebras associated with extended Dynkin quivers
• A theory of generalized Donaldson-Thomas invariants. II. Multiplicative identities for Behrend functions
• N=2 Quantum Field Theories and Their BPS Quivers
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Cluster algebras I: Foundations
• Quivers with potentials and their representations I: Mutations
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• A theory of generalized Donaldson-Thomas invariants

Cited by

• Algebraicity and Asymptotics: An explosion of BPS indices from algebraic generating series
• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies
• Superconformal Index, BPS Monodromy and Chiral Algebras
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I

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• The quiver approach to the BPS spectrum of a 4d N=2 gauge theory
• Geometric engineering of (framed) BPS states