Radon Transforms and the SYK model

TL;DR

This paper explores how Radon transforms applied to Laplace eigenfunctions in hyperbolic space relate to the SYK model, revealing geometric insights into boundary conditions for four-point functions.

Contribution

It demonstrates the interpretation of Radon transforms in hyperbolic space using the Poincare disc model, connecting geometric boundary conditions to the SYK model.

Findings

Radon transform clarifies boundary conditions in SYK four-point functions

Poincare disc model simplifies interpretation of the Radon map

Eigenfunctions' geometric origin is elucidated

Abstract

Motivated by recent work on the Sachdev-Ye-Kitaev (SYK) model, we consider the effect of Radon or X-ray transformations, on the Laplace eigenfunctions in hyperbolic Bolyai-Lobachevsky space. We show that the Radon map from this space to Lorentzian-signature Anti-de Sitter or de Sitter space is easier to interpret if we use the Poincare disc model and eigenfunctions rather than the upper-half-plane model. In particular, this version of the transform reveals the geometric origin of the boundary conditions imposed on the eigenfunctions that are involved in calculating the SYK four-point function.