paper

de Sitter at all loops: the story of the Schwinger model

arXiv:2403.16166 · doi:10.1007/JHEP08(2024)155

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.

28 pages + (29 pages of appendices), 2 figures; v2 notation improved, references added, typos fixed, calculations streamlined; v3 further clarifications added and some minor typos fixed. Additionally an important typo was corrected in section 4.2 ensuring an SO(3) invariant final answer; v4/v5 typos fixed, added missing contact term in Electric Field 2 point function, published version

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