Topological Terms and the Misner String Entropy

TL;DR

This paper explores how topological renormalization and additional topological terms in AdS gravity influence the thermodynamics and entropy of Misner strings in Taub-NUT-AdS and Taub-Bolt-AdS spacetimes, with implications for holography.

Contribution

It applies topological renormalization to compute Misner string entropy and investigates the effects of Chern-Pontryagin terms on boundary parity-odd contributions.

Findings

Topological renormalization correctly accounts for physical quantities in the parity-preserving sector.

Misner string entropy is computed using topological methods.

Adding Chern-Pontryagin invariant introduces parity-odd effects in the boundary stress tensor.

Abstract

The method of topological renormalization in anti-de Sitter (AdS) gravity consists in adding to the action a topological term which renders it finite, defining at the same time a well-posed variational problem. Here, we use this prescription to work out the thermodynamics of asymptotically locally anti-de Sitter (AlAdS) spacetimes, focusing on the physical properties of the Misner strings of both the Taub-NUT-AdS and Taub-Bolt-AdS solutions. We compute the contribution of the Misner string to the entropy by treating on the same footing the AdS and AlAdS sectors. As topological renormalization is found to correctly account for the physical quantities in the parity preserving sector of the theory, we then investigate the holographic consequences of adding also the Chern-Pontryagin topological invariant to the bulk action; in particular, we discuss the emergence of the parity-odd contribution in the boundary stress tensor.