Studies in: entanglement entropy of two dimensional quasi-topological quantum field theory and geometry of the exact renormalization group and higher spin holography

Weiss, Alexander Beer

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https://hdl.handle.net/2142/89044 Copy

Description

Title

Studies in: entanglement entropy of two dimensional quasi-topological quantum field theory and geometry of the exact renormalization group and higher spin holography

Author(s)

Weiss, Alexander Beer

Issue Date

2015-12-04

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

Leigh, Robert G.

Doctoral Committee Chair(s)

Ryu, Shinsei

Committee Member(s)

• Fradkin, Eduardo
• Yang, Liang

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• entanglement entropy
• quasi-topological quantum field theory
• matrix product states
• exact renormalization group
• higher spin holography

Abstract

Part I: Entanglement Entropy of 2d Quasi-Topological Quantum Field Theory We compute the entanglement entropy of two-dimensional quasi-topological 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 space-time, 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 Wilson-Polchinski exact renormalization group (RG) applied to the generating functional of single-trace operators at a free-fixed point in d = 2 + 1 dimensions. By exploiting the rich symmetry structure of free-field theory, we study the geometric nature of the RG equations and the associated Ward identities. The geometry, as expected, is holographic, with anti-de 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 on-shell 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 Vasiliev-type 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].

Graduation Semester

2015-12

Type of Resource

text

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http://hdl.handle.net/2142/89044

Copyright and License Information

Copyright 2015 Alexander B. Weiss

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