Topological terms and the Misner string entropy

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