Quantum line defects and refined BPS spectra

  • Michele CiraficiEmail author


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.


Supersymmetric field theory Wilson-’t Hooft line operators Donaldson-Thomas invariants K-theory Quiver representation theory 

Mathematics Subject Classification

14N35 81T13 81T60 



I am grateful to Michele del Zotto, Vivek Shende, Yan Soibelman, Vasily Pestun, and Johannes Wälcher for discussions. I am thankful to the organizers of the program Symplectic Geometry and Representation Theory at the Hausdorff Institute for Mathematics in Bonn for the warm hospitality during the last stages of this project. These results were presented at the workshops Geometry and Topology inspired by Physics in 2018 in Ascona and Young Researchers in String Mathematics in 2017 in Bonn, and I am grateful to the organizers for the invitation to speak and for the warm hospitality. I am a member of INDAM-GNFM, I am supported by INFN via the Iniziativa Specifica GAST and by the FRA2018 project “K-theoretic Enumerative Geometry in Mathematical Physics”.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e GeoscienzeUniversità di TriesteTriesteItaly
  2. 2.INFN, Sezione di TriesteTriesteItaly
  3. 3.Institute for Geometry and Physics (IGAP)TriesteItaly

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