Constructive Tensorial Group Field Theory II: The U(1)-T⁴₄ Model

2015/10/16 by Vincent Lahoche, Lahoche, Vincent
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions

paper · doi:10.48550/arxiv.1510.05051

openalex publication_date 2015/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we continue our program of non-pertubative constructions of tensorial group field theories (TGFT). We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian U(1) gauge invariance, nicknamed U(1)-T⁴₄. We use a multiscale loop vertex expansion. It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.

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