An algebraic approach to the large N renormalization group flow of φ4-theory

by Nadia Flodgren (Stockholm University)

Wednesday 18 Dec 2024, 13:00 → 16:00 Europe/Stockholm

FB54 (AlbaNova Main Building)

Abstract
This thesis investigates the role of non-associative algebras in the renormalization group flow of multiscalar theories in the
large N limit. Renormalization group (RG) flow describes how the parameters of a quantum field theory (QFT) vary with
the energy scale, which is useful for identifying theories with special symmetries. The large N limit is an approximation in
which QFT calculations simplify, and by not explicitly relying on perturbation theory it can even yield non-perturbative
results.
The leading order RG flow of multiscalar theories in four dimensions can be described with non-associative algebras,
which our research shows is particularly useful in the large N limit. Based on the algebraic description and simple scaling
arguments we have developed a method for identifying sets of large N models that are well behaved to at least leading
loop order. The novelty of the method lies in it not relying on diagrammatic or combinatorial analysis. For several models
we have identified sets of large N limits which include known limits, such as the melonic limit of tensor models, and new
limits with intriguing properties, yet to be analyzed to higher loop order. The algebraic approach, if further developed, has
the potential of simplifying calculations and deepening our understanding of QFT in the large N limit and in general.