Chern-Simons action for inhomogeneous Virasoro group as an extension of three dimensional flat gravity

TL;DR

This paper develops a Chern-Simons action for an inhomogeneous Virasoro group, extending 3D flat gravity models and resembling higher-spin theories, with potential applications in gravitational physics.

Contribution

It introduces a novel Chern-Simons formulation based on the semi-direct sum of the Virasoro algebra and its coadjoint representation, extending flat gravity models.

Findings

Constructs a new Chern-Simons model for inhomogeneous Virasoro group

Extends flat gravity theories beyond standard formulations

Highlights limitations for cosmological constant deformations

Abstract

We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity.