Supersymmetric Sachdev-Ye-Kitaev models
Abstract
We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) 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 nonperturbatively 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.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Inst. for Advanced Study, Princeton, NJ (United States)
- Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1423995
- Alternate Identifier(s):
- OSTI ID: 1339477
- Grant/Contract Number:
- SC0009988
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 2; Related Information: A small addendum was made to the original version - see doi 10.1103/PhysRevD.95.069904; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, and Sachdev, Subir. Supersymmetric Sachdev-Ye-Kitaev models. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.95.026009.
Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, & Sachdev, Subir. Supersymmetric Sachdev-Ye-Kitaev models. United States. doi:10.1103/PhysRevD.95.026009.
Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, and Sachdev, Subir. Fri .
"Supersymmetric Sachdev-Ye-Kitaev models". United States. doi:10.1103/PhysRevD.95.026009. https://www.osti.gov/servlets/purl/1423995.
@article{osti_1423995,
title = {Supersymmetric Sachdev-Ye-Kitaev models},
author = {Fu, Wenbo and Gaiotto, Davide and Maldacena, Juan and Sachdev, Subir},
abstractNote = {We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) 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 nonperturbatively 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.},
doi = {10.1103/PhysRevD.95.026009},
journal = {Physical Review D},
number = 2,
volume = 95,
place = {United States},
year = {2017},
month = {1}
}
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