Holographic dual of the five-point conformal block

Abstract

We present the holographic object which computes the five-point global conformal block in arbitrary dimensions for external and exchanged scalar operators. This object is interpreted as a weighted sum over infinitely many five-point geodesic bulk diagrams. These five-point geodesic bulk diagrams provide a generalization of their previously studied fourpoint counterparts. We prove our claim by showing that the aforementioned sum over geodesic bulk diagrams is the appropriate eigenfunction of the conformal Casimir operator with the right boundary conditions. This result rests on crucial inspiration from a much simpler p-adic version of the problem set up on the Bruhat-Tits tree.

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

“…Indeed, the proof presented here follows closely the procedure used in Ref. [70] in the context of the five-point block.…”

“…We now turn our attention to the six-point con- The procedure leading to its holographic representation, as discussed below, follows closely the strategy discussed in Ref. [70] in the context of the five-point block.…”

“…To keep the discussion short, we refer the reader to Refs. [14,70] for more details on the embedding space formalism as it relates to the proof by conformal Casimir. Indeed, the proof presented here follows closely the procedure used in Ref.…”

“…Using the definition of F ∆ C ,∆ R and the explicit forms forK and ξ in embedding space (see appendix B.1), this can easily be computed to give (suppressing the arguments of F ∆ C ,∆ R ) [70],…”

The boundary theory of a spinor field theory on the Bruhat-Tits tree

“…The AdS/CFT correspondence on T p is proposed in [6,7]. Some further developments are given in [8][9][10][11][12][13][14][15][16][17][18][19][20][21] Zabrodin only considered a massless scalar field. Recently, the spinor field theory on T p has been proposed by Gubser, Jepsen and Trundy [15].…”