# The Bulk Dual of SYK: Cubic Couplings

## TL;DR

This paper derives the bulk dual description of the SYK model by analyzing correlation functions to determine the masses and cubic couplings of bulk fields, advancing the understanding of holography in this context.

## Contribution

It systematically constructs the bulk theory of the SYK model by extracting operator dimensions and three-point functions from correlation functions, revealing the structure of bulk cubic couplings.

## Key findings

- Derived the spectrum of bulk fields from SYK correlators
- Computed cubic couplings of bulk fields and analyzed their structure
- Simplified the couplings for large q regimes

## Abstract

The SYK model, a quantum mechanical model of $N \gg 1$ Majorana fermions $\chi_i$, with a $q$-body, random interaction, is a novel realization of holography. It is known that the AdS$_2$ dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the $1/N$ expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large $N$ dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large $q$.