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Entropy variations and light ray operators from replica defects

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [2];  [2]
  1. University of Illinois at Urbana-Champaign, IL (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
  2. University of California, Berkeley, CA (United States)
  3. University of Illinois at Urbana-Champaign, IL (United States)
+ Show Author Affiliations
We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d - 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.
Research Organization:
University of California, Oakland, CA (United States); University of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Organization:
National Science Foundation (NSF); US Department of Defense (USDOD); USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
AC02-05CH11231; SC0019183; SC0019380
OSTI ID:
1976547
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2022; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

References (48)

Defects in conformal field theory journal April 2016
Relative entropy of excited states in two dimensional conformal field theories journal July 2016
Geometric and renormalized entropy in conformal field theory journal August 1994
Medicine and the future of health: reflecting on the past to forge ahead journal October 2016
Line defects in the 3d Ising model preprint January 2013
Boundary and Interface CFTs from the Conformal Bootstrap text January 2015
Modular Hamiltonian of Excited States in Conformal Field Theory text January 2015
Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields journal January 2018
The light-ray OPE and conformal colliders journal January 2021
Relative entanglement entropies in 1 + 1-dimensional conformal field theories journal February 2017
Bootstrapping the 3d Ising twist defect journal March 2014
Bulk emergence and the RG flow of entanglement entropy journal May 2015
Boundary and interface CFTs from the conformal bootstrap journal May 2015
Line defects in the 3d Ising model journal July 2013
Rényi entropy and conformal defects journal July 2016
Relative entropy of excited states in two dimensional conformal field theories journal July 2016
Generalized gravitational entropy journal August 2013
Quantum corrections to holographic mutual information journal August 2016
Nonlinear gravity from entanglement in conformal field theories journal August 2017
Spinning operators and defects in conformal field theory journal August 2019
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal September 2016
Universality at large transverse spin in defect CFT journal September 2018
A general proof of the quantum null energy condition journal September 2019
Bounds for OPE coefficients on the Regge trajectory journal October 2017
Light-ray operators in conformal field theory journal November 2018
Recovering the QNEC from the ANEC journal May 2020
Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence journal March 2001
Aspects of holographic entanglement entropy journal August 2006
A covariant holographic entanglement entropy proposal journal July 2007
Conformal collider physics: energy and charge correlations journal May 2008
Entanglement entropy and quantum field theory journal June 2004
Entanglement entropy of two disjoint intervals in conformal field theory: II journal January 2011
Modular Hamiltonians on the null plane and the Markov property of the vacuum state journal August 2017
Quantum null energy condition, entanglement wedge nesting, and quantum focusing journal January 2020
Proof of the generalized second law for rapidly evolving Rindler horizons journal December 2010
Entanglement Rényi entropies in holographic theories journal December 2010
Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices journal May 2012
Entanglement entropy across a deformed sphere journal February 2015
Some results on the shape dependence of entanglement and Rényi entropies journal February 2015
Entropy on a null surface for interacting quantum field theories and the Bousso bound journal April 2015
Proof of the quantum null energy condition journal January 2016
Quantum focusing conjecture journal March 2016
Holographic proof of the quantum null energy condition journal July 2016
Gravitational dual of the Rényi displacement operator journal August 2017
Local modular Hamiltonians from the quantum null energy condition journal March 2018
Energy density from second shape variations of the von Neumann entropy journal October 2018
Modular Hamiltonian for Excited States in Conformal Field Theory journal July 2016
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal May 2006

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
boundary quantum field theory
conformal field theory
field theories in higher dimensions