A stochastic analysis approach to tensor field theories
File(s)
Accepted version
Author(s)
Chandra, Ajay
Ferdinand, Léonard
Type
Journal Article
Abstract
We present two different arguments using stochastic analysis to construct super-renormalizable tensor field theories, namely the T4/3 and T4/4 models. The first approach is the construction of a Langevin dynamic [15 , 23 ] combined with a PDE energy estimate while the second is an application of the variational approach of Barashkov and Gubinelli [ 3]. By leveraging the melonic structure of divergences, regularizing properties of non-local products, and controlling certain random operators, we demonstrate that for tensor field theories these approaches can be significantly simplified in comparison to what is required for Φ4/d models.
Date Acceptance
2025-02-14
Citation
L'Institut Henri Poincare, Annales B: Probabilites et Statistiques
ISSN
0246-0203
Publisher
Institute of Mathematical Statistics
Journal / Book Title
L'Institut Henri Poincare, Annales B: Probabilites et Statistiques
Copyright Statement
Subject to copyright. This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
Publication Status
Accepted