Chern-Simons-like Theories of Gravity

TL;DR

This thesis explores a broad class of 3D massive gravity models reformulated as Chern-Simons-like theories, enabling a unified Hamiltonian analysis and revealing models free of ghosts with favorable holographic properties.

Contribution

It introduces a general Chern-Simons-like formulation for 3D massive gravity models, extending known theories and analyzing their physical and holographic characteristics.

Findings

Models are free of ghost-like scalar excitations

Existence of parameter regions with positive boundary central charge and positive energy

Construction of models with improved holographic behavior

Abstract

In this PhD thesis, we investigate a wide class of three-dimensional massive gravity models and show how most of them (if not all) can be brought in a first-order, Chern-Simons-like, formulation. This allows for a general analysis of the Hamiltonian for this wide class of models. From the Chern-Simons-like perspective, the known higher-derivative theories of 3D massive gravity, like Topologically Massive Gravity and New Massive Gravity, can be extended to a wider class of models. These models are shown to be free of (possibly ghost-like) scalar excitations and exhibit improved behavior with respect to Anti-de Sitter holography; the new models have regions in their parameter space where positive boundary central charge is compatible with positive mass and energy for the massive spin-2 mode. We discuss the construction of several of these improved models in detail and derive the necessary constraints needed to remove any unphysical degree of freedom. We also comment on the AdS/LCFT correspondence which arises when the massive spin-2 mode becomes massless and is replaced by a logarithmic mode. Most of the results have been published elsewhere, however, a special effort is made here to present the aspects of Chern-Simons-like theories in a pedagogical and comprehensive way.