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Title:  Studies in: entanglement entropy of two dimensional quasitopological quantum field theory and geometry of the exact renormalization group and higher spin holography 
Author(s):  Weiss, Alexander Beer 
Director of Research:  Leigh, Robert G. 
Doctoral Committee Chair(s):  Ryu, Shinsei 
Doctoral Committee Member(s):  Fradkin, Eduardo; Yang, Liang 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  entanglement entropy
quasitopological quantum field theory matrix product states exact renormalization group higher spin holography 
Abstract:  Part I: Entanglement Entropy of 2d QuasiTopological Quantum Field Theory We compute the entanglement entropy of twodimensional quasitopological quantum field the ories (QTFTs). These are theories in which the correlation functions depend on the topology and on the total area of the underlying spacetime, but are blind to all local details of the geometry, and include topological quantum field theory (TFT) as their limiting case. We use two complimentary methods to compute the entanglement entropy; the first method is the replica trick and the other is to devise a novel tensor network representation, or more precisely, matrix product state (MPS) representation, of the quantum states of QTFT. We demonstrate that the two calculations are in agreement. Part II: Geometry of the Exact Renormalization Group and Higher Spin Holography We consider the WilsonPolchinski exact renormalization group (RG) applied to the generating functional of singletrace operators at a freefixed point in d = 2 + 1 dimensions. By exploiting the rich symmetry structure of freefield theory, we study the geometric nature of the RG equations and the associated Ward identities. The geometry, as expected, is holographic, with antide Sitter spacetime emerging correspondent with RG fixed points. In particular, we are able to cast the renormalization group equations as Hamilton equations of radial evolution in AdSd+1. We solve these bulk equations of motion in terms of a boundary source and derive an onshell bulk action. We demonstrate that it correctly encodes all of the correlation functions of the field theory, written as “Witten diagrams.” Going further, we show that the field theory construction gives us a par ticular vector bundle over the (d + 1)dimensional RG mapping space, called a jet bundle, whose structure group arises from the bilocal transformations of the bare fields in the path integral. The sources for quadratic operators constitute a connection on this bundle and a section of its endomor phism bundle. We make comparisons to Vasilievtype higher spin theories. Detailed calculations are carried out for the case of Majorana fermions. Results and comments are presented for complex scalars. Additional details can be found in [1, 2]. 
Issue Date:  20151204 
Type:  Text 
URI:  http://hdl.handle.net/2142/89044 
Rights Information:  Copyright 2015 Alexander B. Weiss 
Date Available in IDEALS:  20160302 
Date Deposited:  201512 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois