Final PhD Oral Examination (Thesis Title: “2+1d Quantum Field Theories in Large N Limit”)

Speaker: 
HAMID OMID
Event Date and Time: 
Fri, 2016-12-16 11:00 - 13:00
Location: 
Room 318, Hennings Building
Local Contact: 
Physics and Astronomy, UBC
Intended Audience: 
Public

Abstract:
Quantum field theories have been essential tools for studying various physical
systems in the past century. In this thesis, we will focus on the quantum field theories
in 2+1d. Quantum field theories in 2+1d are of particular interest as they are between
1+1d quantum field theories that enjoy infinite tower of symmetries and 3+1
dimensional quantum field theories that mean-field-theory approximation works well at.
In this thesis, we show that Large N expansion is a powerful tool which in regimes that
the system is interacting strongly could be used as an alternative to coupling expansion
scheme.
In Chapter 2, we consider a quantum field theory in 3+1d with the defect of a
large number of fermion flavors, N. We study the next-to-leading order contributions to
the fermions current-current correlation function by performing a large N expansion.
We find that the next-to-leading order contributions to the current-current correlation
function is significantly suppressed. The suppression is a consequence of a surprising
cancellation between the two contributing Feynman diagrams. We calculate the
model's conductivity via the Kubo formula and compare our results with the observed
conductivity for graphene.
In Chapter 3, we study graphene's beta function in large N. We use the large
N expansion to explore the renormalization of the Fermi velocity in the screening
dominated regime of charge neutral graphene with a Coulomb interaction. We show
that inclusion of the fluctuations of the magnetic field leads to a cancellation of the beta
function to the leading order in 1/N. The first non-zero contribution to the beta function
turns out to be of order 1/N2.
In Chapter 4, we study the phase structure of a phi-six theory in large N. The
leading order of the large N limit of the O(N) symmetric phi-six theory in three
dimensions has a phase which exhibits spontaneous breaking of scale symmetry
accompanied by a massless dilaton. In this chapter, we show that this ``light dilaton'' is
actually a tachyon. This indicates an instability of the phase of the theory with
spontaneously broken approximate scale invariance. We rule out the existence of
Bardeen-Moshe-Bander phase.

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