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Title: 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:
 [1];  [2];  [3];  [4]
  1. Harvard Univ., Cambridge, MA (United States)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  3. Inst. for Advanced Study, Princeton, NJ (United States)
  4. 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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