Note on global symmetry and SYK model

  • Junyu LiuEmail author
  • Yehao Zhou
Open Access
Regular Article - Theoretical Physics


The goal of this note is to explore the behavior of effective action in the SYK model with general continuous global symmetries. A global symmetry will decompose the whole Hamiltonian of a many-body system to several single charge sectors. For the SYK model, the effective action near the saddle point is given as the free product of the Schwarzian action part and the free action of the group element moving in the group manifold. With a detailed analysis in the free sigma model, we prove a modified version of Peter-Weyl theorem that works for generic spin structure. As a conclusion, we could make a comparison between the thermodynamics and the spectral form factors between the whole theory and the single charge sector, to make predictions on the SYK model and see how symmetry affects the chaotic behavior in certain timescales.


2D Gravity AdS-CFT Correspondence Black Holes 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  2. 2.Institute for Quantum Information and Matter, California Institute of TechnologyPasadenaU.S.A.
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  4. 4.Department of Physics & AstronomyUniversity of WaterlooWaterlooCanada

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