A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

TL;DR

This paper constructs a conformally invariant scalar two-point function on the Berger sphere, utilizing boundary value problem techniques, with potential applications in AdS/CFT correspondence.

Contribution

It introduces a method to derive conformally invariant two-point functions on the Berger sphere using boundary operators, expanding tools for holographic and conformal geometry studies.

Findings

The two-point function is conformally invariant.

It corresponds to a boundary operator of conformal dimension one.

The methods may be applicable in broader AdS/CFT contexts.

Abstract

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.