Nut Charge, Anti-de Sitter Space and Entropy

TL;DR

This paper tests whether entropy in ALAdS spacetimes with nut charge receives contributions from Misner strings in addition to bolt areas, by constructing Taub-NUT-AdS and Taub-Bolt-AdS solutions and computing their thermodynamics. A general entropy formula incorporating bolt and Misner-string contributions is derived, and the Taub-Bolt-AdS entropy is obtained explicitly, displaying a phase structure and confirming consistency with holographic expectations in the large-squashing limit. The work discusses a potential AdS/CFT dual description on a squashed boundary, using free-field determinants to probe normalization, and highlights the role of Misner strings in holographic entropy beyond supersymmetric setups.

Abstract

It has been proposed that spacetimes with a U(1) isometry group have contributions to the entropy from Misner strings as well as from the area of $d-2$ dimensional fixed point sets. In this paper we test this proposal by constructing Taub-Nut-AdS and Taub-Bolt-AdS solutions which are examples of a new class of asymptotically locally anti-de Sitter spaces. We find that with the additional contribution from the Misner strings, we exactly reproduce the entropy calculated from the action by the usual thermodynamic relations. This entropy has the right parameter dependence to agree with the entropy of a conformal field theory on the boundary, which is a squashed three-sphere, at least in the limit of large squashing. However the conformal field theory and the normalisation of the entropy remain to be determined.

Figures (2)

• Figure 1: The action $I$ as a function of $s$ for $k=1$ and $b^2=9/2\pi$, as given by equation (\ref{['eqn:TBAdS_action']}). The zero is at $s=3+\sqrt{10}$.
• Figure 2: The temperature $T=1/\sqrt{E}$ as a function of $s$ for $k=1$ and $b^2=9/2\pi$. The minimum value is at $s=2+\sqrt{3}$.