Abstract
We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model. These are quantum mechanical models involving 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 model with a single supercharge has unbroken supersymmetry at large , but nonperturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large equation, and also by performing numerical computations for small values of . We also compute the large spectrum of “singlet” operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an 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 computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.
- Received 10 November 2016
- Corrected 16 March 2017
DOI:https://doi.org/10.1103/PhysRevD.95.026009
© 2017 American Physical Society
Physics Subject Headings (PhySH)
Corrections
16 March 2017