  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.
