Related papers: Approximations for strongly-coupled supersymmetric…
Gauge theories represent a fundamental framework underlying modern physics, constituting the basis of the Standard Model and also providing useful descriptions of various phenomena in condensed matter. Realizing gauge theories on accessible…
The (2+1)-dimensional Thirring model is studied by using the Gaussian approximation method in the functional Schr\"odinger picture. Although the dynamical symmetry breaking does not occur in the large N limit, it does occur in the Gaussian…
We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well…
We demonstrate how the fundamental supersymmetric theory at high energy scales can be reconstructed using precision data expected at future high energy collider experiments. We have studied a set of representative examples in this context:…
We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal…
In higher-dimensional supersymmetric theories gauge couplings of the effective four-dimensional theory are determined by expectation values of scalar fields. We find that at temperatures above a critical temperature $T_*$, which depends on…
Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the…
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
It is generally known for $\mathrm{U}(N)$ gauge theory at finite temperature that phase transitions are manifested by taking the large-$N$ limit. Since the large-$N$ theory undergoes two thermodynamic phase transitions, a nontrivial…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
We study dynamics of two-dimensional non-abelian gauge theories with N=(0,2) supersymmetry that include N=(0,2) supersymmetric QCD and its generalizations. In particular, we present the phase diagram of N=(0,2) SQCD and determine its…
By performing the matrix integral over the tree level superpotential of N=1 supersymmetric SO(N)/Sp(N) gauge theories obtained from N=2 SQCD by adding the mass term for the adjoint scalar field, the exact effective superpotential in terms…
We describe a numerical method which allows us to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent…
We develop Coulomb gas pictures of strong and weak coupling regimes of supersymmetric Yang-Mills theory in five and four dimensions. By relating them to the matrix models that arise in Chern-Simons theory, we compute their free energies in…
One of the much-debated novel features of theories with extra dimensions is the presence of power-like loop corrections to gauge coupling unification, which have the potential of allowing a significant reduction of the unification scale. A…
The frozen Gaussian approximation provides a highly efficient computational method for high frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly hyperbolic…
We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from cosmological constant. These theories have discrete gauge symmetries…
A detailed analysis is given of the effects of common and recurring approximations used in conventional superconductivity theories on the condensation energy values, whose magnitudes are notoriously smaller than those of other energies as…
A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing $N$ massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability…