The bulk dual of SYK: cubic couplings

By D. Gross, V. Rosenhaus. 2017

177 citations recorded by the source corpus.

A bstractThe SYK model, a quantum mechanical model of N ≫ 1 Majorana fermions χi, 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/de514f6f99433a625e375ab7e6336b6c1e899e9b

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In Nuclear and High Energy Physics

Citations in the corpus

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “(An explicit calculation for n = 3 was done in [37].”
The Schwarzian theory — origins (2018, background): “Sachdev-Ye-Kitaev (SYK) models of N Majorana fermions with random all-to-all interactions have received a host of attention in the past few years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], mainly due to the appearance of maximally chaotic behavior [13, 14, 15, 16, 17], suggesting a 2d holographic dual”
All point correlation functions in SYK (2017, methodology): “In [6] we computed the contact diagram exactly, whereas the planar diagram was evaluated in the large q limit, in which the computation simplifies.”
An introduction to the SYK model (2018, background): “nd three-point functions of the Oh, respectively. The masses are related to the dimensions in the standard way, m2 n = h(h 1), while the cubic couplings, in the limit n;m;k˛1 where they simplify, are [41,68], nmkˇ (n+ m+ k)! ( n+ m k+ 1 2 )( m+ k n+ 1 2 )( k+ n m+ 1 2 ) : (5.2) One could similarly t”
Towards a full solution of the large N double-scaled SYK model (2018, methodology): “also theories with similar behavior to SYK, but without disorder [16{18]. The relation of SYK to random matrix theory was discussed in { 1 { [19,20]. Higher correlation functions were studied as well [21,22], and results beyond the leading order in Nwere obtained [23{25]. One usually studies the SYK”
Three dimensional view of the SYK/AdS duality (2017, unknown): “In particular it would be interesting if the three point function of bi-locals [70] has a related 3d interpretation.”