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

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.

1+49 pages, no figures. v2: Several typos corrected

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• An embedding formalism for CFTs in general states on curved backgrounds
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
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• A Note on Scalar Field Theory in AdS_3/CFT_2