arXiv subjects

Joona Oikarinen

Publications and source records attributed to Joona Oikarinen.

4 recordsLinked to original sources

arXiv2025

Small deviations of Gaussian multiplicative chaos and the free energy of the two-dimensional massless Sinh--Gordon model

We prove a global decomposition result for $\log$-correlated Gaussian fields on the $d$-dimensional torus and use this to derive new small deviations bounds for a class of Gaussian multiplicative chaos measures obtained from Gaussian fields with zero spatial mean on the $d$-dimensional torus. The upper bound is obtained by a modification of the method that was used in \cite{LRV}, and the lower bound is obtained by applying the Donsker--Varadhan variational formula. We also give the probabilistic path integral formulation of the massless Sinh--Gordon model on a torus of side length $R$, and study its partition function as $R$ tends to infinity. We apply the small deviation bounds for Gaussian multiplicative chaos to obtain lower and upper bounds for the logarithm of the partition function, leading to the existence of a non-zero and finite subsequential infinite volume limit for the free energy.

math-ph↗

arXiv2022

Stress-Energy in Liouville Conformal Field Theory on Compact Riemann Surfaces

We derive the conformal Ward identities for the correlation functions of the Stress--Energy tensor in probabilistic Liouville Conformal Field Theory on compact Riemann surfaces by varying the correlation functions with respect to the background metric. The conformal Ward identities show that the correlation functions of the Stress--Energy tensor can be expressed as a differential operator with meromorphic coefficient acting on the correlation functions of the primary fields of Liouville Conformal Field Theory. Variations of the metric come in three different forms: reparametrizations, conformal scalings and deformations of the conformal structure. Conformal symmetry makes it easy to treat variations of the metric that do not deform the conformal structure. Variations that deform the conformal structure have to be treated separately, and this part of the computation relies on regularity and integrability properties of the correlation functions of Liouville Conformal Field Theory.

math-ph↗

arXiv2020

Stress-Energy in Liouville Conformal Field Theory

We construct the stress-energy tensor correlation functions in probabilistic Liouville Conformal Field Theory (LCFT) on the two-dimensional sphere by studying the variation of the LCFT correlation functions with respect to a smooth Riemannian metric. In particular, we derive conformal Ward identities for these correlation functions. This forms the basis for the construction of a representation of the Virasoro algebra on the canonical Hilbert space of the LCFT. In \cite{ward} the conformal Ward identities were derived for one and two stress-energy tensor insertions using a different definition of the stress-energy tensor and Gaussian integration by parts. By defining the stress-energy correlation functions as functional derivatives of the LCFT correlation functions and using the smoothness of the LCFT correlation functions proven in \cite{Oik} allows us to control an arbitrary number of stress-energy tensor insertions needed for representation theory.

math-ph↗

arXiv2019

Smoothness of correlation functions in Liouville Conformal Field Theory

In this article we prove smoothness of the correlation functions in probabilistic Liouville Conformal Field Theory. Our result is a step towards proving that the correlation functions satisfy the higher Ward identities and the higher BPZ equations, predicted by the Conformal Bootstrap approach to Conformal Field Theory.

math-ph↗