Summing inflationary logarithms in nonlinear sigma models

• Published in: The journal of high energy physics 2022-03, Vol.2022 (3), p.69-39, Article 69
• Main Authors: Miao, S. P., Tsamis, N. C., Woodard, R. P.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Curvature; Elementary Particles; Gravity; High energy physics; Logarithms; Models of Quantum Gravity; Nonperturbative Effects; Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; Sigma Models; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2022)069

A bstract We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the “tail” part of the propagator and can be summed using a variant of Starobinsky’s stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders.