# Accession Number:

## AD1052096

# Title:

## Supersymmetric SYK Models

# Descriptive Note:

## Journal Article - Open Access

# Corporate Author:

## Harvard University Department of Physics, Cambridge United States

# Personal Author(s):

# 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.

# Descriptors:

# Subject Categories:

- Nuclear Physics and Elementary Particle Physics
- Theoretical Mathematics