Note on global symmetry and SYK model

Abstract

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.

44 pages

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Cited by in corpus (9)

• Defects in Jackiw-Teitelboim Quantum Gravity
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• Warped Schwarzian theory
• A One-Loop Test of the near-AdS${}_2$/near-CFT${}_1$ Correspondence
• Scrambling and decoding the charged quantum information
• Holographic boundary states and dimensionally-reduced braneworld spacetimes
• SYK Model with global symmetries in the double scaling limit