Naked singularities and the Wilson loop

TL;DR

This paper explores dualities involving geometric theories, focusing on how Wilson loop calculations in spacetimes with naked singularities resemble those in black hole spacetimes, indicating they reflect metric parameters rather than horizon features.

Contribution

It demonstrates that Wilson loop results in naked singularity spacetimes mimic black hole cases, suggesting boundary observables depend on metric parameters, not horizons.

Findings

Wilson loop calculations in naked singularity spacetimes resemble black hole results.

Boundary quark potential reflects metric parameters, not horizon presence.

Wilson loops capture metric information rather than true horizon features.

Abstract

We give observations about dualities where one of the dual theories is geometric. These are illustrated with a duality between the simple harmonic oscillator and a topological field theory. We then discuss the Wilson loop in the context of the AdS/CFT duality. We show that the Wilson loop calculation for certain asymptotically AdS scalar field spacetimes with naked singularities gives results qualitatively similar to that for the AdS black hole. In particular, it is apparent that (dimensional) metric parameters in the singular spacetimes permit a ``thermal screening'' interpretation for the quark potential in the boundary theory, just like black hole mass. This suggests that the Wilson loop calculation merely captures metric parameter information rather than true horizon information.