Aspects of quantum field theory, holography and de Sitter

Karydas, Matthaios

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https://hdl.handle.net/2142/125545 Copy

Description

Title

Aspects of quantum field theory, holography and de Sitter

Author(s)

Karydas, Matthaios

Issue Date

2024-07-02

Director of Research (if dissertation) or Advisor (if thesis)

Draper, Patrick Ian

Doctoral Committee Chair(s)

Faulkner, Thomas

Committee Member(s)

• Witek, Helvi
• Noronha, Jorge Leite

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Quantum Field Theory
• Holography
• dS/CFT
• Effective Field Theory
• Schwarzschild-de Sitter
• de Sitter
• Constrained State
• f(Riemann) gravity
• Discontinuous lapse
• Entropy of SdS
• Bubble Nucleation
• Hartle-Hawking state
• Back-reaction
• Weyl-Fefferman-Graham
• Weyl-ambient metric
• Weyl geometry
• Holographic Weyl anomaly
• Weyl cohomology
• Weyl connection
• Weyl structure
• conformal ladder graph
• fishnet model
• Thermal field theory
• infinite resummation of ladder diagrams

Abstract

This thesis explores several topics in Euclidean gravitational path integral, holography and quantum field theory. We first examine factorization and continuity properties of fields in the Euclidean gravitational path integral for actions constructed from powers of the Riemann tensor. We find the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. Our work shows that the constrained state idea for the Euclidean Schwarzschild-de Sitter (SdS) geometry is robust against at least some types of quantum corrections from heavy fields. As an application of our construction, we compute the entropy of SdS in D = 4 using the BTZ method. We then discuss gravitational back-reaction in the semiclassical treatment of quantum fields near black hole horizons in $D$ dimensions. Motivated by the Cohen-Kaplan-Nelson bound, we construct states that deviate significantly from the Hartle-Hawking state and determine the conditions under which the energy density of theses states have large back-reaction on the background geometry. We find the characteristic energy scale $~(r_{s}^2 G_{N})^{1/D}$ with $r_{s}$ the Schwarzschild radius of the black hole. Our analysis suggests that well-controlled effective field theory outside the black hole can only account for an entropy that scales as $A^{\frac{D-2}{2}}$, where $A$ is the area of the black hole horizon in Planck units. Next, we analyze the problem of bubble nucleation in gravitational context. We consider the setting where a true vacuum bubble nucleates inside a false vacuum region. We approximate the spacetimes in the true and false regions as de Sitter spaces in static slicing, with different cosmological constants. A novel point aspect of our construction is that we allow the lapse degree of freedom on the bubble to remain unfixed. We derive the Israel junction conditions across the bubble and determine the bubble's effective action. We confirm that the bubble's effective action reproduces the junction conditions and use this effective action to analyze bubble nucleation. Within the framework of Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence we analyze the recently introduced Weyl-Fefferman-Graham (WFG) gauge. In the WFG gauge, both a metric and a Weyl connection are induced at the conformal boundary and conformal geometry is upgraded to Weyl geometry. We present in detail the geometric ingredients of Weyl geometry, such as Weyl-covariant tensors. We study the holographic Weyl anomaly in this context, focusing on its cohomological properties. We compute the Weyl anomaly for $2d,4d$-dimensional boundaries and interestingly find the WFG gauge only trivially modifies the Weyl anomaly cocycle in the FG gauge. Motivated by the WFG gauge we then generalize the ambient metric construction of Fefferman-Graham for conformal manifolds to a corresponding construction for Weyl manifolds, referred to as the Weyl-ambient construction. This is achieved by promoting a conformal manifold into a Weyl manifold by assigning a Weyl connection to the principal $\mathbb{R}_+$-bundle, realizing a Weyl structure. We then show that the Weyl structure admits a well-defined initial value problem, which determines the Weyl-ambient metric. Through the Weyl-ambient construction, we also investigate Weyl-covariant tensors on the Weyl manifold and explicitly define the extended Weyl-obstruction tensors. The Weyl-ambient construction places the WFG gauge into a solid geometric framework. In the final chapter of this thesis we investigate a recently discovered connection between certain $L$-loop conformal ladder graphs and thermal expectation values of a $U(1)$ charge of a free massive complex scalar $\phi(x)$ in $d=2L+1$ dimensions. We broaden this correspondence by showing that the the free energy itself corresponds to a certain $L$-loop conformal ladder graph which evaluates a certain four-point function of the singular two-dimensional conformal fishnet model of Kazakov and Olivucci. Thermal partition functions offer a novel new perspective on conformal graphs. As an application of this point of view we reproduce the resummation of an infinite number of loop diagrams through the language of thermal partition functions.

Graduation Semester

2024-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/125545

Copyright and License Information

Copyright 2024 Matthaios Karydas

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