title: Aspects of Tensor Models and Tensor Field Theories
creator: Keppler, Hannes
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
subject: ddc-530
subject: 530 Physics
description: This thesis investigates random tensor models and their applications across quantum field theory. Originating in quantum gravity studies, tensor models provide a framework for generating discrete random geometries and have connections to several other fields, including topology, conformal field theory, and constructive field theory. Their extension to d-dimensional quantum field theories constitutes tensor field theories. The most important feature of tensor models is their melonic large N limit. The 1/N expansion allows for non-trivial and systematic resummations of correlation functions, making them interesting quantum field theory models. Other methods that are used in this thesis include combinatorics, asymptotic series analysis, and two-particle irreducible effective action techniques.  Three main themes are developed throughout this work. First, the research on tensor models with symplectic symmetry broadens our understanding of tensor models with various symmetry groups. We establish a formal relation between orthogonal and symplectic random tensor models, demonstrating that tensor models with O(N) symmetry are related to corresponding models with Sp(N) symmetry through the replacement N to -N. This duality extends to tensors transforming in arbitrary finite-dimensional representations of these groups and provides a framework for new fermionic models. Second, we analyze the zero-dimensional O(N ) vector model using constructive field theory techniques, particularly the Loop Vertex Expansion, establishing analyticity and Borel summability properties of the free energy. We derive transseries expansions that incorporate both perturbative and non-perturbative contributions. Third, we study a four-dimensional O(N)³ tensor field theory exhibiting asymptotic freedom in the ultraviolet while developing strong correlations in the infrared. Through numerical solution of the Schwinger–Dyson equations, we demonstrate how quantum fluctuations significantly modify the propagator and identify a threshold mass below which the running coupling diverges at a finite infrared scale.
date: 2025
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserver/36949/1/Dissertation_Keppler_Hannes.pdf
identifier: DOI:10.11588/heidok.00036949
identifier: urn:nbn:de:bsz:16-heidok-369495
identifier:   Keppler, Hannes  (2025) Aspects of Tensor Models and Tensor Field Theories.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/36949/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng