Abstract
We consider the two-dimensional Schwinger model of a massless charged fermion coupled to an Abelian gauge field on a fixed de Sitter background. The theory admits an exact solution, first examined by Jayewardena, and can be analyzed efficiently using Euclidean methods. We calculate fully non-perturbative, gauge-invariant correlation functions of the electric field as well as the fermion and analyze these correlators in the late-time limit. We compare these results with the perturbative picture, for example by verifying that the one-loop contribution to the fermion two-point function, as predicted from the exact solution, matches the direct computation of the one-loop Feynman diagram. We demonstrate many features endemic of quantum field theory in de Sitter space, including the appearance of late-time logarithms, their resummation to de Sitter invariant expressions, and Boltzmann suppressed non-perturbative phenomena, with surprising late-time features.
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Acknowledgments
It is a pleasure to acknowledge Atsushi Higuchi for reinvigorating our interest in solvable QFTs in de Sitter and Christoph Adam for generously sharing his PhD thesis with us. We also thank Paolo Benincasa, Pietro Benetti Genolini, Vasileios Letsios, Manuel Loparco, Beatrix Muhlmann, Guilherme Pimentel, Ben Pethybridge, Jiaxin Qiao, Vladimir Schaub, Zimo Sun, and Kamran Salehi Vaziri for useful discussions. We would also like to thank Johnny Brendan Gleeson for pointing out important sign mistakes in an earlier draft of this paper. D.A. is funded by the Royal Society under the grant “Concrete Calculables in Quantum de Sitter” and the STFC Consolidated grant ST/X000753/1. T.A. is supported by the UKRI Future Leaders Fellowship “The materials approach to quantum spacetime” under reference MR/X034453/1. A.R.F. is funded by the Royal Society under the grant “Boundaries and Defects in Quantum Field Theory and Gravity.”
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Anninos, D., Anous, T. & Fukelman, A.R. De Sitter at all loops: the story of the Schwinger model. J. High Energ. Phys. 2024, 155 (2024). https://doi.org/10.1007/JHEP08(2024)155
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DOI: https://doi.org/10.1007/JHEP08(2024)155