skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Equivalent equations of motion for gravity and entropy

Abstract

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Authors:
 [1];  [1]; ORCiD logo [1];  [1];  [2]
  1. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics. Physics Dept.
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States). Theory Group
Publication Date:
Research Org.:
Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE; The Netherlands Organisation for Scientific Research (NWO) (Netherlands)
OSTI Identifier:
1353113
Grant/Contract Number:
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory

Citation Formats

Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James. Equivalent equations of motion for gravity and entropy. United States: N. p., 2017. Web. doi:10.1007/JHEP02(2017)004.
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, & Sully, James. Equivalent equations of motion for gravity and entropy. United States. doi:10.1007/JHEP02(2017)004.
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James. Wed . "Equivalent equations of motion for gravity and entropy". United States. doi:10.1007/JHEP02(2017)004. https://www.osti.gov/servlets/purl/1353113.
@article{osti_1353113,
title = {Equivalent equations of motion for gravity and entropy},
author = {Czech, Bartlomiej and Lamprou, Lampros and McCandlish, Samuel and Mosk, Benjamin and Sully, James},
abstractNote = {We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.},
doi = {10.1007/JHEP02(2017)004},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4works
Citation information provided by
Web of Science

Save / Share:
  • Papapetrou's equations of motion of a spinning particle in general relativity are extended to the case of a nonsymmetric stress-energy tensor in order to include the test particle's self-gravity. There are derivations of the spin tensor and the momentum tensor and their equations of motion, including gravitational radiation reaction. There is a treatment of a test particle with self-gravity charge, and electromagnetic moment. The dynamical role of the test particle's self-gravity is illustrated in the weak-field approximation. The principal conclusion is that the test particle's Newtonian gravitational potential energy contributes to the test particle's inertial mass (under electromagnetic forces) inmore » the same way as do other forms of mass-energy (rest mass, internal energy, and kinetic energy).« less
  • A general method for determining the structure of the gravitational equations of motion is presented in the fourth-order theory of gravity based on local conformal Weyl invariance of the gravitational action. The explicit structure for these equations is given for a time-dependent, spherically symmetric geometry. 8 refs.
  • The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discussmore » an example of such a trajectory in the space containing the c {le} 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models.« less