Author ORCID Identifier

https://orcid.org/0000-0002-4934-2955

Year of Publication

2020

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Physics and Astronomy

First Advisor

Dr. Sumit R. Das

Abstract

We study (nearly) AdS/CFT holography within the context of the Sachdev-Ye- Kitaev (SYK) model. We present a systematic procedure to extract the dynamics of the low energy Schwarzian mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the infrared within the framework of perturbation theory. We develop a systematic approach using Feynman diagrams in bilocal theory to obtain a formal expression for the enhanced and O(1) corrections to the bilocal propagator and apply this general technique to large q SYK. We show that the Schwarzian theory describes a sector of a general class of two dimensional CFTs using conformal bootstrap techniques. We also provide a gravitational interpretation of this fact by showing that the dynamics in the near horizon throat of a specific class of BTZ black holes is described very well by Jackiw-Teitelboim (JT) gravity which gives rise to the Schwarzian action. We study the highly nontrivial conformal matter spectrum of the SYK model at arbitrary q. We provide a three dimensional bulk interpretation and carry out Kaluza-Klein (KK) reduction to reproduce the SYK spectrum and more significantly, the conformal bilocal propagator. We provide an interpretation of the two dimensional dual spacetime of the conformal sector of the SYK model using techniques from bilocal holography. We present a resolution of a conundrum about the signature of the dual spacetime using nonlocal integral transformations.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2020.325

Funding Information

This research was supported in part by the Heising-Simons Foundation, the Simons Foundation, and National Science Foundation Grant No. NSF PHY-17489 from July-December 2019.

It was also partially supported by the National Science Foundation grant NSF-PHY-1521045 from August-December 2018.

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