Holography and Strongly Coupled Quantum Field Theories

Holography;AdS/CFT;Quantum Field Theory;Strongly Coupled;Bulk Reconstruction;Ising Model;not listed

Anand, NikhilKaplan, Jared D. ;

Johns Hopkins University

关键词: Holography;    AdS/CFT;    Quantum Field Theory;    Strongly Coupled;    Bulk Reconstruction;    Ising Model;    not listed;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/60048/ANAND-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

The holographic principle, which states that observables in quantum gravity are associated with the boundary of spacetime, has played a crucial role in guiding particle physics research over the past couple of decades. The anti-deSitter space/conformal field theory (AdS/CFT) correspondence is an avatar of the holographic principle and provides an operational definition of quantum gravity in AdS space in terms of a dual CFT.This thesis is comprised of two parts, both of which fall under the broad theme of AdS/CFT. The first part is directly related; it is about the construction of observables in the bulk of three-dimensional AdS space in terms of two-dimensional CFT operators. This is a particularly attractive arena to study quantum gravity because two-dimensional CFTs have an enhanced Virasoro symmetry algebra that rigidly fixes correlators that would be otherwise unconstrained in higher dimensions. This part of the thesis focuses on non-perturbatively defining a bulk AdS ;;proto-field;; $phi$ in terms of Virasoro generators acting on a local primary operator $mathcal{O}$. An exciting application of this work would be to study correlators in black hole backgrounds non-pertubatively.The second part is indirectly connected to AdS/CFT, but can stand on its own as a numerical prescription to solve quantum field theories (QFTs). QFTs owe their existence to renormalization group flows that begin at ultraviolet CFTs. This suggests that nontrivial information about the flow is encoded into the data that defines the CFT. Typically, this ;;CFT data;; is comprised of the spectrum of local operators present in the theory and the structure constants of the operator algebra. The second part of the thesis explicates a method inspired by holography called ;;conformal truncation,;; in which CFT data is used to truncate and diagonalize the Hamiltonian in a strongly interacting QFT. I will demonstrate its applicability in two and three dimensions.