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.