This thesis consists of two parts. In the first part we consider vortices which are
topological defects that emerge upon spontaneously broken local symmetries in 2 + 1
dimensions. We discuss the renormalization of the central charge and the mass of the
N = 2 supersymmetric Abelian vortices. At the classical level the mass of the vortex is
equal to its central charge, which is referred to as Bogomol’nyi - Prasad - Sommerfield
(BPS) saturation. At the quantum level both the mass and the central charge get
corrections. We show that the mass and the central charge of the vortex get the same
nonvanishing quantum corrections, which preserves BPS saturation at the quantum
In the second part, we study the stochastic background of gravitational waves (SBGW)
generated by kinks and cusps on cosmic string loops. Cosmic strings, which can be
considered as 2+1 dimensional vortices extended along the additional dimension, are one
dimensional topological defects predicted by a large class of unified theories as remnants
of spontaneously broken local or global symmetries. Grand unified theories have gauge
symmetries which are eventually spontaneously broken down to the symmetry of the
Standard Model, and certain class of these phase transitions are expected to produce
cosmic strings. The interactions of cosmic strings result in cusps or kinks on them which
decay by radiating gravitational waves. In this study, we find that kinks contribute at the
same order as cusps to the SBGW, and discuss the accessibility of the total background
due to kinks as well as cusps to current and planned gravitational wave detectors,
as well as to the big bang nucleosynthesis (BBN), the cosmic microwave background
(CMB), and pulsar timing constraints. Furthermore we consider anisotropies in the
SBGW arising from random fluctuations in the number of sources. Such anisotropies are
analogous to the anisotropies observed in the CMB radiation and would carry additional
information about the gravitational-wave sources that generated them.
University of Minnesota Ph.D. dissertation. February 2012. Major: Physics. Advisor: Vuk Mandic. 1 computer file (PDF); vii, 92 pages, appendices I-II.
Critical Vortices in 2+1 dimensions and stochastic background of gravitational waves from cosmic strings..
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