2026-09-21T00:43:07Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/113937 2023-07-11 col_2142_5131 com_2142_5130

2024-04-29T21:47:53Z 2021-07-19 Faulkner, Thomas Leigh, Robert G Bradlyn, Barry Cooper, S Lance Balakrishnan, Srivatsan 2022-04-29T21:41:38Z 2022-04-29T21:41:38Z 2021-12 In the first few chapters of the thesis, we will study defect CFT methods based on the replica trick for characterizing quantum information in quantum field theories. We calculate a coefficient that characterizes the strength of the two point function of the displacement operator in the replica twist defect placed in a holographic CFT, which controls the second order shape dependence of Renyi entropy. We introduce defect CFT methods for calculating correlation functions involving the modular Hamiltonian together with probe operators inserted at lightcone separation. We use these methods to further calculate correlation functions involving modular flows of these probe operators. Tomita-Takesaki theory constrains these correlation functions, which when combined with our defect CFT calculations, provides a proof of the Quantum Null Energy Condition. In the last few chapters of this thesis, we will calculate entanglement measures for states that are defined by a Euclidean path integral together with a source for an operator inserted in the path integral. We provide a purely Lorentzian formula for the modular Hamiltonians for these states for flat entangling cuts which systematizes the task of writing time-ordered expressions for relative entropy of these states with respect to the vacuum to all orders in the source. We further apply this method to calculate a formula for shape deformed modular Hamiltonian for the vacuum state to all orders in the shape deformation. In the case of null shape deformation, we recover the formula for the vacuum modular Hamiltonian for null cuts. We then calculate the shape deformation of relative entropy and provide evidence for the presence of a shock in the stress tensor expectation value when one performs the Connes cocycle flow of the state. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2023-12-01 The student, Srivatsan Balakrishnan, accepted the attached license on 2021-07-16 at 15:10. The student, Srivatsan Balakrishnan, submitted this Dissertation for approval on 2021-07-16 at 15:25. This Dissertation was approved for publication on 2021-07-19 at 10:22. DSpace SAF Submission Ingestion Package generated from Vireo submission #16990 on 2022-04-06 at 17:16:09 Made available in DSpace on 2022-04-29T21:41:38Z (GMT). No. of bitstreams: 3 BALAKRISHNAN-DISSERTATION-2021.pdf: 1599101 bytes, checksum: d792f9c44d65709a36b613ef97e5253c (MD5) THESIS_SB_SOURCE(2).zip: 3117854 bytes, checksum: 14a8b991ed2288a0b92e00aea18108a9 (MD5) LICENSE.txt: 4219 bytes, checksum: 6111f9e0090b89fbbe4fca84e650d207 (MD5) Previous issue date: 2021-07-19 Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:41:44Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:42:24Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:43:01Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:44:44Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:46:25Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 123298 Lift date: 2024-04-29T21:47:53Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only application/pdf http://hdl.handle.net/2142/113937 en Copyright 2021 Srivatsan Balakrishnan Entanglement, Quantum Field Theory, QFT, QNEC, Energy Conditions, Path Integral On defect CFT and path integral methods for entanglement in quantum field theories text Thesis Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.