A Stochastic Analysis Approach to Tensor Field Theories

2023/06/08 by Chandra, Ajay, Ferdinand, Léonard
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.05305

Abstract

We present two different arguments using stochastic analysis to construct super-renormalizable tensor field theories, namely the T⁴₃ and T⁴₄ models. The first approach is the construction of a Langevin dynamic combined with a PDE energy estimate while the second is an application of the variational approach of Barashkov and Gubinelli. By leveraging the melonic structure of divergences, regularising properties of non-local products, and controlling certain random operators, we demonstrate that for tensor field theories these arguments can be significantly simplified in comparison to what is required for Φ⁴_d models.

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