Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory

TL;DR

This paper investigates the renormalization of a five-dimensional quartic tensor field theory, establishing its asymptotic freedom and developing a Hopf algebraic framework to understand its combinatorial structure.

Contribution

It introduces a Hopf algebraic structure for the renormalization of the 5D quartic tensor model and analyzes Hochschild cohomology and Dyson-Schwinger equations at multiple loops.

Findings

Confirmed asymptotic freedom of the model

Defined a Connes-Kreimer-like Hopf algebra for the model

Analyzed Hochschild cohomology and Dyson-Schwinger equations

Abstract

This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes-Kreimer-like Hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail, at one- and two-loop levels, the Hochschild cohomology allowing to write the combinatorial Dyson-Schwinger equations. Feynman tensor graph Hopf subalgebras are also exhibited.