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

Lukas Müller; Richard J. Szabo; Lóránt Szegedy

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arXiv · 1907.04734

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

Lukas Müller·Richard J. Szabo·Lóránt Szegedy

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Abstract

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to 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.

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Lukas Müller, Richard J. Szabo, Lóránt Szegedy. 2019-07-10. Symmetry defects and orbifolds of two-dimensional Yang-Mills theory. https://arxiv.org/abs/1907.04734

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