BMS field theories and Weyl anomaly

Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

Geodesic distance: A descriptor of geometry and correlator of pregeometric density of spacetime events

Classical geometry can be described either in terms of a metric tensor [Formula: see text] or in terms of the geodesic distance [Formula: see text]. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum structure of spacetime. This is because one can incorporate some of the key quantum effects by replacing [Formula: see text] by another function [Formula: see text] such that [Formula: see text] is nonzero. This allows one to introduce a zero-point-length in the spacetime. I show that the geodesic distance can be an emergent construct, arising in the form of a correlator [Formula: see text], of a pregeometric variable [Formula: see text], which can be interpreted as the quantum density of spacetime events. This approach also shows why null surfaces play a special role in the interface of quantum theory and gravity. I describe several technical and conceptual aspects of this construction and discuss some of its implications.

GR and classical mechanics: Magic?

A new fundamental ingredient is introduced in the study of Asymptotically Flat Einstein–Maxwell Spacetimes, namely the change of coordinate systems from the standard ones constructed from the infinite number of possible Bondi null surfaces to those based on the four complex-parameter set, [Formula: see text], of Asymptotically Shear–Free (ASF) null surfaces. ASF coordinate systems are determined by “world-lines” in the parameter space, [Formula: see text]. Setting a Weyl tensor component, defined as the complex-mass-dipole, to zero, a unique complex center of mass/charge “world-line” is obtained. From this line and Bianchi identities, much of classical mechanics is directly obtained: spin, orbital angular momentum, kinematic momentum, angular momentum conservation, energy–momentum conservation, Newton’s second law with Abraham–Lorentz–Dirac radiation reaction, Rocket force and Dirac g-factor.

The atoms of space, gravity and the cosmological constant

I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations arise from maximizing the density of states of matter plus geometry. The former is identified using the thermodynamics of null surfaces while the latter arises due to the existence of a zero-point length in the spacetime. The resulting field equations remain invariant when a constant is added to the matter Lagrangian, which is a symmetry of the matter sector. Therefore, the cosmological constant arises as an integration constant. A nonzero value [Formula: see text] of the cosmological constant renders the amount of cosmic information [Formula: see text] accessible to an eternal observer finite and hence is directly related to it. This relation allows us to determine the numerical value of [Formula: see text] from the quantum structure of spacetime.