Schwarzian Field Theory at High Temperatures

Ilya Losev

arXiv:2607.29423v1 Primary: math.PR Secondary: math-ph

Abstract

In this work we study the high-temperature limit of the Schwarzian Field Theory probability measure. We show that on large scales this limit concentrates on jump processes, while its small-scale behaviour is governed by a process which we call Schwarzian Field Theory on the real line. This Schwarzian Theory on the real line can be viewed as the infinite-volume version of the Schwarzian Field Theory. In addition to showing this local convergence, we also provide a systematic treatment of the Schwarzian Theory on the real line. This includes the calculation of the correlation functions and a corresponding uniqueness theorem.

Disclosure

“w Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK. E-mail: ilya.losev@maths.ox.ac.uk. AI disclosure: In this work, AI tools were used solely for proofreading and linguistic refinement. 1”
PDF page 1

Classification: Proofreading, grammar, or spelling
Multiplier: 1
Verified: 2026-08-23T19:15:37.195715Z

Structural counts

Pages 41 pdf

Theorems 8 source

Lemmas 10 source

Propositions 11 source

Corollaries 3 source

Definitions 5 source

Displayed equations 210 source

Bibliography entries 28 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Schw_high_temp.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.