Note on global symmetry and SYK model
- Creators
-
Liu, Junyu
- Zhou, Yehao
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.
Additional Information
© 2019 The Author(s). 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. Received: February 28, 2019; Revised: April 30, 2019; Accepted: May 10, 2019; Published: May 17, 2019. We thank Jordan Cotler, Dionysios Anninos, Nicholas Hunter-Jones, Davide Gaiotto, Yingfei Gu, John Preskill, Subir Sachdev, David Simmons-Duffin, Douglas Stanford, Beni Yoshida and Yi-Zhuang You for discussions and suggestions. JL especially thanks Douglas Stanford for his help on understanding the one-loop determinants of N = 2 supersymmetric SYK model and complex SYK models, and comments on the charge sectors. JL also acknowledges Yingfei Gu for his valuable discussions on the charge sectors of complex SYK models. JL is supported in part by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support from the Gordon and Betty Moore Foundation (GBMF-2644), and by the Walter Burke Institute for Theoretical Physics. YZ is supported by the graduate student program at the Perimeter Institute.Attached Files
Published - Liu-Zhou2019_Article_NoteOnGlobalSymmetryAndSYKMode.pdf
Submitted - 1901.05666.pdf
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Additional details
- Eprint ID
- 95598
- Resolver ID
- CaltechAUTHORS:20190520-103300835
- Institute for Quantum Information and Matter (IQIM)
- NSF
- PHY-1125565
- Gordon and Betty Moore Foundation
- GBMF-2644
- Walter Burke Institute for Theoretical Physics, Caltech
- Perimeter Institute
- Created
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2019-05-20Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics