A stochastic control approach to Euclidean field theories with exponential interaction

Abstract: In this talk, I demonstrate how to obtain couplings of the Liouville field and the sinh-Gordon field with the Gaussian free field in dimension $d=2$, such that the difference is in a Sobolev space of regularity $\alpha>1$. The analysis covers the entire $L^2$ phase. The main tool is the variational approach to Euclidean field theories by Barashkov and Gubinelli applied to field theories with exponential interaction. The additional key ingredients are estimates for the short scales of the minimizer of the variational problem and several applications of the Brascamp-Lieb inequality.

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields

Series comments: Paweł Duch (EPFL) will give a mini-course on "Singular Stochastic PDEs", in the period March 9-20, 2026. Further information can be found here: www.math.sissa.it/course/phd-course/singular-stochastic-pdes. You can follow the course online here: sissa-it.zoom.us/j/84337146226?pwd=SMrOupIjXvQ2pwrc6djLExOCKZPbKZ.1. Please email Ilya Chevyrev for the Zoom passcode.