Exploring effective descriptions of gauge fields and strings : A Lagrangian approach with insights from color-kinematics duality

Sammanfattning: The concept of a color-kinematics duality is an important driving force in advancing the modern understanding of scattering amplitudes, in both field theory and string theory. Yet, open questions remain that motivate the need for a deeper understanding of the duality. A central open question is: do the kinematic numerators admit a Lie-algebraic origin, just like the corresponding color factors? The answer may be intimately related to a detailed understanding of the duality at the level of the Lagrangian. For pure Yang-Mills theory, a cubic Lagrangian which directly computes color-dual numerators is not yet known. In this thesis, we make progress in this direction by constructing a cubic Lagrangian in terms of the ordinary gauge field and a set of auxiliary fields. The contributions to the numerators are split into independent sectors specified by the number of contractions between polarization vectors. We find a novel Lagrangian with a finite number of fields and interactions that computes color-dual Yang-Mills numerators to any multiplicity, valid for sectors with up to two polarization contractions. In the context of string theory, insights from the color-kinematics duality have revealed interesting relations between string and field theory amplitudes. The sector of open bosonic string amplitudes where transcendental numbers are absent is known to be described by a higher-derivative field theory. The spectrum of this theory includes a massless gauge field and extra massive modes: by integrating the latter out from the Lagrangian, we obtain an expansion in the inverse string tension, which is a low-energy effective description of the dynamics of the massless modes of the bosonic string. This thesis develops the general method and explicitly writes down the operators entering the effective Lagrangian through fourth order in the inverse string tension.