Accession Number:

AD1052096

Title:

Supersymmetric SYK Models

Descriptive Note:

Journal Article - Open Access

Corporate Author:

Harvard University Department of Physics, Cambridge United States

Report Date:

2017-03-04

Pagination or Media Count:

36.0

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.

Subject Categories:

  • Nuclear Physics and Elementary Particle Physics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE