Holography and Quaternionic Taub-NUT

TL;DR

This paper explores the holographic properties of quaternionic Taub-NUT space, a four-dimensional manifold interpolating between AdS_4 and a coset space, using twistor methods to construct propagators for potential dual CFT correlation calculations.

Contribution

It introduces a novel application of holography to quaternionic Taub-NUT space and constructs explicit propagators using twistor techniques for future correlation function analysis.

Findings

Constructed bulk-to-bulk and bulk-to-boundary propagators for conformally coupled scalars.

Demonstrated the interpolation of scalar curvature sign change at the boundary.

Provided a framework for calculating dual CFT correlators on a squashed S^3.

Abstract

As a concrete application of the holographic correspondence to manifolds which are only asymptotically Anti-de Sitter, we take a closer look at the quaternionic Taub-NUT space. This is a four dimensional, non-compact, inhomogeneous, riemannian manifold with the interesting property of smoothly interpolating between two symmetric spaces, AdS_4 itself and the coset SU(2,1)/U(2). Even more interesting is the fact that the scalar curvature of the induced conformal structure at the boundary (corresponding to a squashed three-sphere) changes sign as we interpolate between these two limiting cases. Using twistor methods, we construct the bulk-to-bulk and bulk-to-boundary propagators for conformally coupled scalars on quaternionic Taub-NUT. This may eventually enable us to calculate correlation functions in the dual strongly coupled CFT on a squashed S^3 using the standard AdS/CFT prescription.