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Title: Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

Abstract

We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε, turning them into a simple diagrammatic perturbation theory at large central charge.Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of themore » soft mode. These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.« less

Authors:
 [1];  [2];  [2]
  1. Inst. for Advanced Study, Princeton, NJ (United States); Univ. of British Columbia, Vancouver, BC (Canada)
  2. Univ. of British Columbia, Vancouver, BC (Canada)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1596287
Grant/Contract Number:  
SC0009988; PHY-1748958
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal Field Theory; 1/N Expansion; Field Theories in Higher Dimensions; AdS-CFT Correspondence

Citation Formats

Haehl, Felix M., Reeves, Wyatt, and Rozali, Moshe. Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs. United States: N. p., 2019. Web. doi:10.1007/JHEP11(2019)102.
Haehl, Felix M., Reeves, Wyatt, & Rozali, Moshe. Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs. United States. doi:https://doi.org/10.1007/JHEP11(2019)102
Haehl, Felix M., Reeves, Wyatt, and Rozali, Moshe. Mon . "Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs". United States. doi:https://doi.org/10.1007/JHEP11(2019)102. https://www.osti.gov/servlets/purl/1596287.
@article{osti_1596287,
title = {Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs},
author = {Haehl, Felix M. and Reeves, Wyatt and Rozali, Moshe},
abstractNote = {We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε, turning them into a simple diagrammatic perturbation theory at large central charge.Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode. These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.},
doi = {10.1007/JHEP11(2019)102},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2019,
place = {United States},
year = {2019},
month = {11}
}

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