Citation
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. https://resolver.caltech.edu/CaltechTHESIS:06072016152814803
Abstract
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 welldefined 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 welldefined UV completion. For small regions $R$, these constraints translate into integrated positivity conditions of the bulk stressenergy 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): 
 
Group:  Caltech Theory  
Thesis Committee: 
 
Defense Date:  7 June 2016  
Funders: 
 
Record Number:  CaltechTHESIS:06072016152814803  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:06072016152814803  
DOI:  10.7907/Z9ZW1HW3  
Related URLs: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9852  
Collection:  CaltechTHESIS  
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. 439kB 
Repository Staff Only: item control page