Critical Vortices in 2 + 1 dimensions and Stochastic Background of Gravitational Waves from Cosmic Strings

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 level.;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.