Synopsis: The advantage of sizing down one dimension
Gravity in four dimensions continues to elude a full quantum formulation and treatment. Hope persists that lower dimensional versions of gravity, while different in important respects from the physically relevant case, may provide important lessons. In a paper appearing in Physical Review D, Alexander Maloney of McGill University, Canada, Wei Song of the Chinese Academy of Sciences in Beijing, and Andrew Strominger at Harvard University, US, report comprehensive results on a version of gravity in three dimensions that promises to be amenable to a full quantum treatment.
The version of gravity studied by Maloney et al. contains two terms in addition to the minimal Einstein-Hilbert action: a negative cosmological constant term and a Chern-Simons term. Naively, the parameters denoting the strength of these interactions are arbitrary. One of the key results of their paper is that the product of the cosmological constant and Chern-Simons coupling constant is not only bounded from below but should assume its lowest possible value in order for the theory to be well-behaved and stable. Going beyond analyzing the classical theory, the paper presents a suggestive quantum calculation that hints that the theory is equivalent to a two-dimensional chiral conformal field theory—a much anticipated result. – Ansar Fayyazuddin