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The method of topological renormalization in anti-de Sitter (AdS) gravityconsists 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 thisprescription to work out the thermodynamics of asymptotically locally anti-deSitter (AlAdS) spacetimes, focusing on the physical properties of the Misnerstrings of both the Taub-NUT-AdS and Taub-Bolt-AdS solutions. We compute thecontribution of the Misner string to the entropy by treating on the samefooting the AdS and AlAdS sectors. As topological renormalization is found tocorrectly account for the physical quantities in the parity preserving sectorof the theory, we then investigate the holographic consequences of adding alsothe Chern-Pontryagin topological invariant to the bulk action; in particular,we discuss the emergence of the parity-odd contribution in the boundary stresstensor.

Topological Terms and the Misner String Entropy