Cosmological Topologically Massive Gravitons and Photons

TL;DR

This work analyzes cosmological topologically massive gravity in AdS$_3$, showing that linearized bulk excitations possess a chirality-dependent mass splitting but a single positive-energy degree of freedom for finite topological mass $\mu$. The theory can be recast as a pair of SL$(2,\mathbb{R})$ Chern–Simons theories with boundary central charges, with special critical points where one central charge vanishes and gravity becomes equivalent to topologically massive electrodynamics, yet bulk wave packets remain nontrivial. Finite-energy AdS$_3$ wave packets exist across the parameter range, and at the critical point $\mu=1$ there is a gravity–photon duality yielding exact AdS$_3$ pp-wave solutions, linking bulk dynamics to boundary CFT structure. The results illuminate how a cosmological constant and topological mass restructure the spectrum, asymptotics, and boundary charges, with implications for bulk/boundary dualities and the stability of the theory.

Abstract

We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative SL(2,R) Chern--Simons theories, weighted by the central charges of the boundary conformal field theory. At two particular "critical" values of the couplings, one of these central charges vanishes, and linearized topologically massive gravity becomes equivalent to topologically massive electromagnetism; however, the physics of the bulk wave packets remains unaltered here.

Figures (1)

• Figure 1: A 2d cross-section---corresponding to $V = 0$ in the ambient four-dimensional coordinates, or equivalently $t=0$ in Poincaré coordinates---of the Poincaré patch, showing how it sits in the hyperboloid model of AdS$_3$. The surface $z=0$ lies in the AdS$_3$ boundary. The $z=\infty$ surface intersects any constant-Poincaré-time slice in a pair of lines through the bulk, as shown; these meet asymptotically (to the left, in the picture) in a single point on the boundary.