Dimensional reduction along the RG flow in combinatorially non-local field theories

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Abstract

Combinatorially non-local interactions are at the heart of matrix and tensor theories as well as non-commutative field theory. Interestingly, for theories on a compact domain their renormalization group equations are non-autonomous in the momentum scale. We show that this should be regarded not as an issue but as a feature of such theories leading to a reduction of the effective dimension of the field theory along the renormalization group flow. We illustrate this with the example of a field theory with tensorial symmetry using the functional renormalization group in the cyclic-melonic potential approximation. While this yields a dimensional flow on compact domain, we also find a new phase structure with hints for an asymptotic safe fixed point in the large-volume limit.

Speakers from the University of Münster

Thürigen, Johannes

Professur für Reine Mathematik (Prof. Wulkenhaar)

Projects the talk is about

Non-perturbative Group field theory from combinatorial Dyson-Schwinger equations and their algebraic structure Duration: 01/06/2019 - 12/08/2022 | 1st Funding period Funded by: DFG - Individual Grants Programme Type of project: Individual project

Publications referred to in the talk

Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models Pithis AG, Thürigen J (2020) In: ((Bitte Journal prüfen)), 12 (2020). doi:10.1007/JHEP12(2020)159 Research article (journal) | Peer reviewed | Published