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Abelian Duality for Generalized Maxwell Theories

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Abstract

We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon of abelian duality for local observables in these theories as a form of Fourier duality, relating observables in theories with dual abelian gauge groups and inverted coupling constants in a way compatible with the local structure. We give a description of expectation values in this theory and prove that duality preserves expectation values. Duality is shown to, for instance, interchange higher analogues of Wilson and ’t Hooft operators.

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Acknowledgments

I would like to thank Kevin Costello for many helpful ideas and discussions throughout this project, and Thel Seraphim for some of the initial ideas on how to view abelian duality for expectation values as a version of Plancherel’s theorem. I would also like to thank Saul Glasman, Sam Gunningham, Owen Gwilliam, Boris Hanin, Theo Johnson-Freyd, David Nadler, Toly Preygel, Nick Rozenblyum and Jesse Wolfson for helpful conversations, and the anonymous referees for many useful comments and corrections. Finally, I’d like to thank Theo Johnson-Freyd, Aron Heleodoro and Philsang Yoo for carefully reading an earlier draft and offering many helpful comments and corrections. Figures were created using the diagramming software Dia.

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  1. Institut des Hautes Études Scientifiques, 35 Route de Chartres, Bures-sur-Yvette, 91440, France

    Chris Elliott

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Correspondence to Chris Elliott.

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Elliott, C. Abelian Duality for Generalized Maxwell Theories. Math Phys Anal Geom 22, 22 (2019). https://doi.org/10.1007/s11040-019-9319-3

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