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

  • Micha Berkooz
  • Prithvi NarayanEmail author
  • Joan Simón
Open Access
Regular Article - Theoretical Physics


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.


1/N Expansion Random Systems 2D Gravity Gauge-gravity correspondence 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Department of PhysicsIndian Institute of TechnologyPalakkadIndia
  3. 3.School of Mathematics and Maxwell Institute for Mathematical SciencesUniversity of EdinburghEdinburghU.K.

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