AEI Golm

In this talk, a concrete realization of the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics in non-abelian gauge theories is presented. The method of Berends-Giele to package Feynman diagrams into currents is shown to yield classical solutions to the non-linear Yang-Mills equations. We describe a non-linear gauge transformation of these perturbiner solutions which reorganize the cubic-diagram content such that the kinematic dependence obeys the same Jacobi identities as the accompanying color factors. The resulting tree-level subdiagrams are assembled to kinematic numerators of tree-level and one-loop amplitudes which satisfy the BCJ duality.

This talk describes a method to compute supersymmetric tree amplitudes and loop integrands in ten-dimensional super Yang-Mills theory. It relies on the constructive interplay between their cubic graph organization and BRST invariance of the underlying pure spinor superspace description. After a general introduction to this kind of superspace, we discuss a canonical set of multiparticle building blocks which represent tree level subdiagrams and are guided by their BRST transformation. These building blocks are shown to yield a compact solution for tree level amplitudes, and the applicability of the BRST approach to loop integrands is exemplified through recent examples at one-loop.

Two classes of solutions of the Einstein equations with symmetry which

are frequently studied are the Bianchi and Gowdy models. The aim of this

talk is to explain certain relations between these two classes of

spacetimes which can provide insights into the dynamics of both. In

particular it is explained that the special case of the Gowdy models known as circular loop spacetimes are Bianchi models in disguise. Generalizations of Gowdy spacetimes which can be thought of as inhomogeneous perturbations of some of the Bianchi models are introduced.

Results concerning their dynamics are presented.