Beta functions and multi-scalar gauge theory

Sammanfattning: In this licentiate thesis, we provide the context and background for our work One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory (published in JHEP) on the renormalization group flow for a multi-scalar SU(N) gauge theory. The background consists of a description of renormalization group flow, with a focus on beta functions andhow to find fixed points, and multi-scalar theories. In the article we perform one-loop betafunction calculations in an adjoint, massless, multi-scalar Yang-Mills theory with a quartic scalar interaction, in four dimensions and at large N. We calculate the coupled renormalization group flows for this theory using an algebraic description we develop. The results show that to one-loop order real fixed points in the parameter space of the scalar coupling and gauge coupling do not occur.