Symmetry defects and orbifolds of two-dimensional Yang–Mills theory

Lukas Müller, Richard J. Szabo, Lóránt Szegedy

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1 Citation (Scopus)
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We describe discrete symmetries of two-dimensional Yang–Mills theory with gauge group G associated with outer automorphisms of G, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted G-bundles and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted G-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang–Mills theory but with gauge group given by an extension of G by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang–Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.
Original languageEnglish
Article number18
JournalLetters in Mathematical Physics
Issue number2
Early online date2 Mar 2022
Publication statusPublished - Apr 2022


  • hep-th
  • math-ph
  • math.DG
  • math.MP
  • math.QA

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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