Schwarzian Field Theory at High Temperatures

Ilya Losev

Schwarzian Field Theory at High Temperatures

Probability 2026-07-31 v1 Mathematical Physics

Authors: Ilya Losev

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.

Keywords

Schwarzian field theory high temperature limit jump processes correlation functions

Cite

@article{arxiv.2607.29423,
  title  = {Schwarzian Field Theory at High Temperatures},
  author = {Ilya Losev},
  journal= {arXiv preprint arXiv:2607.29423},
  year   = {2026}
}