Centrally extended symmetry algebra of asymptotically Goedel spacetimes

TL;DR

This paper derives the asymptotic symmetry algebra of three-dimensional Goedel spacetimes with gauge fields, revealing a centrally extended algebra combining Virasoro and affine symmetries, and identifies conditions for well-defined conserved charges.

Contribution

It introduces the asymptotic symmetry algebra for 3D Goedel spacetimes with gauge fields and demonstrates its central extension structure.

Findings

Asymptotic symmetry algebra is a semi-direct sum of circle diffeomorphisms and two loop algebras.

Conserved charges form a centrally extended algebra combining Virasoro and affine algebras.

Identifies classes of fields with well-defined conserved charges.

Abstract

We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras.