Quantum Line Defects and Refined BPS Spectra

Abstract

In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class $\mathcal{S}$. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the K-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.

28 pages; presentation improved and corrections

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Cited by in corpus (5)

• A slow review of the AGT correspondence
• $q$-nonabelianization for line defects
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• A note on discrete dynamical systems in theories of class $S$
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories