Sarah-Jean Meyer | Searcharxiv

arXiv2026

An FBSDE Construction of the Sine-Gordon EQFT for $β^{2} < \frac{6}{7}\, 8π$ and Perturbative Renormalization in the Full Subcritical Regime

We construct the sine-Gordon measure and its renormalized effective potential in finite volume up to the seventh threshold. The construction relies on a weak stochastic control problem, its associated weak FBSDE, and an analysis of the renormalization flow equation using a multipole Mayer expansion. The analysis is fully inductive, and we include a complete order-by-order analysis in the subcritical regime $β^{2}<8π$.

math-ph↗

arXiv2026

The FBSDE approach to sine-Gordon up to $6π$

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 $β^2 < 6 π$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition $(X_t)_{t \geqslant 0}$ of the interacting Euclidean field $X_{\infty}$ along a scale parameter $t \geqslant 0$. 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, integrability, decay of correlations for local observables, singularity with respect to the free field, Osterwalder-Schrader axioms and other properties.

math-ph↗