Centrally extended symmetry algebra of asymptotically Goedel spacetimes

TL;DR

The paper identifies and analyzes the asymptotic symmetry algebra of three-dimensional Gödel spacetimes in Einstein–Maxwell–Chern–Simons theory. Using a covariant phase-space formalism, it derives a centrally extended algebra, Gödel_3, which is a semi-direct sum of a Witt (Virasoro‑like) algebra with two affine u(1) loop algebras, realized by charges L_n, T_n, and J_n. The central charges are explicitly computed: c = 3αl^2/((1+α^2l^2)G) for the Virasoro sector, with corresponding central terms for the affine sectors, and a field‑dependent construction ensures a well-defined representation on a space of asymptotically Gödel fields that includes Gödel black holes. The results hint at reproducing part of the Gödel black hole entropy via Cardy-like counts and point to future work in supersymmetric extensions and string theory embeddings to fully fix ground states and microstate counting. Overall, the work extends the holographic toolkit to non‑AdS spacetimes with closed timelike curves by revealing a rich, centrally extended symmetry structure at infinity.

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.