The FBDSE approach to sine–Gordon up to 6π

Journal article

We develop a stochastic analysis of the sine-Gordon Euclidean quantum field (cos(βφ))2 on the full space up to the second threshold, i.e. for β 2 < 6π. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition (Xt )t⩾0 of the interacting Euclidean field X∞ along a scale parameter t ⩾ 0. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the interacting field without cut-offs and that it can be used effectively to study the sine-Gordon measure to obtain results about large deviations, sub-gaussian tails, decay of correlations for local observables, singularity with respect to the free field, Osterwalder–Schrader axioms and other properties.

Authors: Gubinelli, M; Meyer, S

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Annals of Probability
• Acceptance date: 2025-11-12
• EISSN: 2168-894X
• ISSN: 0091-1798
• Language: English