The bulk dual of SYK: cubic couplings

The SYK model, a quantum mechanical model of N≫1 Majorana fermions χ_i, with a q-body, random interaction, is a novel realization of holography. It is known that the AdS₂ 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.