Line defects and (framed) BPS quivers

Abstract

The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line defect opens up a new BPS sector: framed BPS states can be bound to the defect. The defect can be geometrically described in terms of laminations on a curve. To a lamination we associate certain elements of the Leavitt path algebra of the BPS quiver and use them to compute the framed BPS spectrum. We also provide an alternative characterization of line defects by introducing framed BPS quivers. Using the theory of (quantum) cluster algebras, we derive an algorithm to compute the framed BPS spectra of new defects from known ones. Line defects are generated from a framed BPS quiver by applying certain sequences of mutation operations. Framed BPS quivers also behave nicely under a set of "cut and join" rules, which can be used to study how N=2 systems with defects couple to produce more complicated ones. We illustrate our formalism with several examples.

80 pages, 16 figures; v2: references added, note added, minor corrections, final version to be published in JHEP

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Cited by in corpus (15)

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• Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
• A slow review of the AGT correspondence
• Quantum Holonomies from Spectral Networks and Framed BPS States
• Aspects of line operators of class S theories
• Generalized quiver mutations and single-centered indices
• $q$-nonabelianization for line defects
• Categorified canonical bases and framed BPS states
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Quivers, Line Defects and Framed BPS Invariants
• Quantum Line Defects and Refined BPS Spectra
• On Framed Quivers, BPS Invariants and Defects
• Toda Systems, Cluster Characters, and Spectral Networks
• BPS Spectra, Barcodes and Walls
• A note on discrete dynamical systems in theories of class $S$