Notes on exchange interactions in holographic p -adic CFT

Abstract

There is a renewed interest in conformal field theories (CFT) on ultrametric spaces (p-adic field and its algebraic extensions) in view of their natural adaptability in the holographic setting. We compute the contributions from the exchange interactions to the four-point correlator of the CFT using Witten diagrams with three-scalar interaction vertex. Together with the contributions from the bulk four-point interaction, the contact term, these provide a complete answer. We remark on the singularity structure in Mellin space, and argue that all these models are analogues of adS 2 /CFT

p-adic Mellin amplitudes

“…4 We should emphasize that what we refer to as the p-adic Mellin amplitude is fundamentally different from what Ref. [47] denotes by the same name. The Mellin variables in our formalism live on a different manifold, and the pole structure of the Mellin amplitudes we derive also differs entirely from the one mentioned in Ref.…”

“…The Mellin variables in our formalism live on a different manifold, and the pole structure of the Mellin amplitudes we derive also differs entirely from the one mentioned in Ref. [47]. 5 More precisely, we assume n + 1 ≥ N , otherwise there are nN − 1 2 (n + 1)(n + 2) conformally invariant cross-ratios (see, e.g.…”

On p-adic string amplitudes in the limit p approaches to one

“…Recently a considerable amount of work has been performed on this topic in the context of the AdS/CFT correspondence [5][6][7][8].…”

Scalar fields on pAdS

“…The application of Q p in the anti-de Sitter/conformal field theory correspondence (AdS/CFT) [11][12][13] begins when the Bruhat-Tits tree (BTtree) is treated as a p-adic version of AdS in [14,15]. More properties of the BTtree are studied based on their work [16][17][18][19][20].…”