A Caltech Library Service

Boundary Relative Entropy as Quasilocal Energy: Positive Energy Theorems and Tomography


Stoica, Bogdan (2016) Boundary Relative Entropy as Quasilocal Energy: Positive Energy Theorems and Tomography. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9ZW1HW3.


We argue that for a spherical region R on the boundary, relative entropy between the vacuum and an arbitrary holographic excited state can be computed in the bulk as a quasilocal energy associated to the volume between R and the minimal surface B̃ ending on the boundary ∂R. Since relative entropy is monotonic and positive in any well-defined quantum theory, the associated quasilocal energy must also be positive and monotonic. This gives rise to an infinite number of constraints on the gravitational bulk, which must be satisfied in any theory of quantum gravity with a well-defined UV completion. For small regions $R$, these constraints translate into integrated positivity conditions of the bulk stress-energy tensor. When the bulk is Einstein gravity coupled to scalar fields, the boundary relative entropy can be related to an integral of the bulk action on the minimal surface B̃. Near the boundary, this expression can be inverted via the inverse Radon transform, to obtain the bulk stress energy tensor at a point in terms of the boundary relative entropy.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:AdS/CFT, holography, string theory, relative entropy, entanglement entropy, quasilocal energy, bulk reconstruction
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Awards:John Stager Stemple Memorial Prize in Physics, 2015
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ooguri, Hirosi
Group:Caltech Theory
Thesis Committee:
  • Ooguri, Hirosi (chair)
  • Schwarz, John H.
  • Marcolli, Matilde
  • Chen, Yanbei
Defense Date:7 June 2016
Funding AgencyGrant Number
Walter Burke Institute of Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Record Number:CaltechTHESIS:06072016-152814803
Persistent URL:
Related URLs:
URLURL TypeDescription of Gravitational Systems from Entanglement of Conformal Field Theories Jennifer Lin, Matilde Marcolli, Hirosi Ooguri, and Bogdan Stoica Phys. Rev. Lett. 114, 221601
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9852
Deposited By: Bogdan Stoica
Deposited On:09 Jun 2016 04:36
Last Modified:28 Oct 2021 19:09

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page