Threelogy in two parts 3-algebras in BLG models and a study of TMG solutions

Abstract

This thesis is a review of research done over the course of the past 4 years, divided into two unrelated parts. The rst is set in the context of Bagger-Lambert-Gustavsson models, based on 3-Lie algebras. In particular I will describe theories with metric 3-algebras of inde nite signature: these present elds with negative kinetic terms. The problem can be solved by gaugeing away the non-physical degrees of freedom, to obtain other well understood theories. I will show how this procedure can be easily applied for 3-algebra metrics of any inde nite signature. Part II of this thesis focuses on solutions of topologically massive gravity (TMG): particular attention is devoted to warped AdS3 black holes, which are discussed in great detail. I will present a novel analysis of the near horizon geometries of these solutions. I further propose an approach for searching for new solutions to 3-dimensional gravity based on conformal symmetry. This approach is able to yield most of the known axisymmetric stationary TMG backgrounds.