Topologically Massive Gravity: Anyon Scattering, Weyl-Gauging and Causality

TL;DR

This thesis explores the properties of Topologically Massive Gravity (TMG), including its Weyl-invariant extensions, particle mass generation, scattering amplitudes, and causality, revealing novel gravitational anyon interactions and symmetry breaking mechanisms.

Contribution

It introduces a Weyl-invariant extension of TMG unifying cosmological TMG and TME, and analyzes particle interactions and causality in 2+1 dimensions, highlighting new mass-spin interactions and symmetry breaking effects.

Findings

Weyl symmetry is spontaneously broken in (A)dS backgrounds.

Masses for spin-2 and spin-1 particles are generated via symmetry breaking.

Gravitational Chern-Simons term induces mass-spin interactions, creating gravitational anyons.

Abstract

In this thesis, we studied the Topologically Massive Gravity (TMG) in two perspectives. Firstly, by using real scalar and abelian gauge fields, we built the Weyl-invariant extension of TMG which unifies cosmological TMG and Topologically Massive Electrodynamics (TME) with a Proca mass term. Here, we have demonstrated that the presence of (Anti)-de Sitter spaces as the background solution, spontaneously breaks the local Weyl symmetry, whereas the radiative corrections at two-loop level breaks the symmetry in flat vacuum. The breaking of Weyl symmetry fixes all the dimensionful parameters and provides masses to spin-2 and spin-1 particles as in the Higgs mechanism. Secondly, we calculated the tree-level scattering amplitude in the cosmological TMG plus the Fierz-Pauli mass term in (Anti)-de Sitter spaces and accordingly found the relevant weak field potential energies between two covariantly conserved localized point-like spinning sources. We have shown that in addition to spin-spin and mass-mass interactions, there also occurs a mass-spin interaction which is generated by the gravitational Chern-Simons term that changes the initial spin of particles converting them to gravitational anyons. In addition to these works concerning TMG, we have also discussed the issue of local causality in $2+1$ dimensional gravity theories and shown that Einstein's gravity, TMG and the new massive gravity are causal as long as the sign of the Newton's constant is set to negative. We study the causality discussion with the Shapiro time delay method.