Supersymmetric Sachdev-Ye-Kitaev models

Abstract

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving N Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The N = 1 model with a single supercharge has unbroken supersymmetry at large N , but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large N equation, and also by performing numerical computations for small values of N . We also compute the large N spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an N = 2 version.In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large N computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.

Supersymmetric SYK model and random matrix theory

“…As is maximally chaotic and nearly conformal, this model could be treated as a holographic dual of quantum black hole with AdS 2 horizon through the (near) AdS/CFT correspondence [11][12][13][14][15][16][17][18][19][20]. In the recent research people have also discussed several generalizations of the SYK model [21][22][23][24], such as higher dimensional generalizations and supersymmetric constraints. Some other related issues and similar models are discussed in .…”

“…The degeneracy of supersymmetric SYK model is also investigated by [24], which we derive again using some different discussion in section 3.2.2. The degeneracy space is enlarged by supersymmetry.…”

“…In order to explore the supersymmetric constraints on the random matrix theory classification, in this paper we will study the symmetry classification and random matrix behavior of the N = 1 supersymmetric extension of SYK model by Fu-Gaiotto-MaldacenaSachdev's prescription [24]. The effect of supersymmetry in the symmetry classification could be summarized in the following aspects,…”

“…Originating from particle physics, supersymmetry will enlarge the global symmetry group in the theory, has fruitful algebras and strong mathematical power used in several models in quantum mechanics and quantum field theory, and is extremely useful to simplify and clarify classical or quantized theories. In the recent study of SYK model, the supersymmetric generalization for the original SYK has been discussed in detail in [24], which shows several different behaviors through supersymmetric extensions. This model might give some implications in the quantum gravity structure of black hole in two dimension in a supersymmetric theory, and also a related conjecture in [57] for spectral form factor and correlation functions in super Yang-Mills theory.…”

The bulk dual of SYK: cubic couplings

“…Or, one can consider a Lorentz invariant higher-dimensional bosonic SYK [30]. For other generalizations, see [19,[50][51][52][53][54][55][56][57][58][59]. In addition, in the study of AdS 2 /CFT 1 one must regulate the bulk, introducing a dilaton and turning it into "nearly" AdS 2 .…”