Supersymmetric Sachdev-Ye-Kitaev models

Fu, Wenbo; Gaiotto, Davide; Maldacena, Juan; Sachdev, Subir

doi:10.1103/PhysRevD.95.026009

Supersymmetric Sachdev-Ye-Kitaev models

Journal Article · Fri Jan 13 00:00:00 EST 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.95.026009· OSTI ID:1423995

Fu, Wenbo ^[1]; Gaiotto, Davide ^[2]; Maldacena, Juan ^[3]; Sachdev, Subir ^[4]

Harvard Univ., Cambridge, MA (United States); Institute for Advanced Study
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)

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.

View Accepted Manuscript (DOE)

Research Organization:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

Grant/Contract Number:: SC0009988

OSTI ID:: 1423995

Alternate ID(s):: OSTI ID: 1339477

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 2 Vol. 95; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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