Supersymmetric SYK 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 coeffixE;cients. 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 xC;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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 04, 2017
- Accession Number
- AD1052096
Entities
People
- Davide Gaiotto
- Juan Maldacena
- Subir Sachdev
- Wenbo Fu
Organizations
- Harvard University
- Institute for Advanced Study
- Perimeter Institute for Theoretical Physics