Bonn 2020 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantum Field Theory

MP 9.2: Talk

Wednesday, April 1, 2020, 11:35–11:55, H-HS VII

Algebraic structure of renormalization in tensorial field theories — •Johannes Thürigen — Mathematisches Institut der Westfälischen Wilhelms-Universität Münster

Quantum field theories on non-commutative geometry have recently been found to be solvable non-perturbatively in a matrix-theory representation. Tensorial field theories are a generalization of such matrix field theory to higher rank and specific models are candidates for a quantum theory of gravity. It is therefore an important question to what extent non-perturbative solutions can be obtained in such field theories as well. I address this challenge making use of the algebraic structure of renormalization. I will derive the Hopf algebra of Feynman diagrams for such non-local field theories giving rise to Dyson-Schwinger equations. This is the first step towards identifying the conditions for solving tensorial field theories non-perturbatively. Control over the non-pertubative regime is an open issue of huge physical interest since the limit to continuum space-time coincides with the limit to critical loci in such approaches to quantum gravity.