Linear bosonic quantum field theories arising from causal variational principles |
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Authors: | Dappiaggi Claudio Finster Felix Oppio Marco |
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Institution: | 1.Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, UK ;2.Maxwell Institute for Mathematical Sciences, Edinburgh, UK ;3.The Higgs Centre for Theoretical Physics, Edinburgh, UK ;4.Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel 11, 15121, Alessandria, Italy ;5.Arnold–Regge Centre, Via P. Giuria 1, 10125, Torino, Italy ;6.University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090, Wien, Austria ;7.Max Planck Institute for Mathematics, Vivatsgasse 7, 53111, Bonn, Germany ; |
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Abstract: | 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. |
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