Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

TL;DR

This paper introduces a new combinatorial approach to compute exact 2-point functions in SYK-like spin glass models, providing insights into bulk reconstruction and low-energy limits.

Contribution

It develops a novel chord diagram combinatorics method to analyze spin glass models and connect them to bulk descriptions in holography.

Findings

Exact 2-point functions computed without Schwinger-Dyson equations

Chord diagram approach relates spin glasses to bulk Hamiltonian

Low energy limit reduces to Schwarzian action

Abstract

The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy limit.