Studies on two topics in theoretical physics: Entanglement entropy and holographic superconductors

This thesis contains two parts. The _rst part consists of the _rst two chapters, studying the entanglement entropy. The second part consists of the third chapter, dealing with holographic superconductors. In chapter one we calculate the topological entanglement entropy of Chern-Simons theories in 2+1 dimensions. We employ a procedure of surgery to do the calculation, and _nd the general formula for the entanglement entropy for any state on any smooth surface. The key component of the result is the so-called S matrices of the WZW models associated with our Chern-Simons theories. We apply our results to the quantum Hall uids that are described by various kinds of Chern-Simons theories and calculate their S matrix elements. In chapter two we study the entanglement entropy for the nontrivial primary states of a two dimensional CFT, the free boson. We use several tricks to help us go through the calculation and get the exact results for several primary states. In chapter three we discuss a model of holographic superconductors. It is a (3+1)- dimensional Abelian-Higgs model of gravity with negative cosmological constant. We study the static, spherically symmetric solutions of this model numerically. These are hairy black holes.The nonzero hair corresponds to the nonzero expectation value of some composite operator in the dual _eld theory. We _nd the second order phase transition at certain critical temperature Tc and a mean _eld critical exponent of 0.5. The low temperature behavior of this model does not conform to that of a superconductor however. We also study the static, axially symmetric solutions (vortex solutions), especially their thermodynamical properties. A numerical algorithm to _nd such solutions is setup, with all the key steps solved.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Dong, Shiying

Contributors dc:contributor

• Leigh, Robert G.
• Katz, Sheldon
• Stone, Michael
• Stack, John D.

• Holographic Superconductors
• Entanglement Entropy

Statement dc:rights

• Copyright 2010 Shiying Dong

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/17070

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/17070