Related papers: String Theory and Integrable Systems
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…
Basic concepts of quantum integrable systems (QIS) are presented stressing on the unifying structures underlying such diverse models. Variety of ultralocal and nonultralocal models is shown to be described by a few basic relations defining…
String theoretical ideas might be relevant for particle physics model building. Ideally one would hope to find a unified theory of all fundamental interactions. There are only few consistent string theories in D=10 or 11 space-time…
The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of…
We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
An exact conformal model representing a constant magnetic field background in heterotic string theory is explicitly solved in terms of free creation/annihilation operators. The spectrum of physical states is examined for different possible…
Cosmic strings are linear concentrations of energy that form whenever phase transitions in the early universe break axial symmetries as originally shown by Kibble. They are the result of frustrated order in the quantum fields responsible…
An overview of supersymmetry and its different applications is presented. We motivate supersymmetry in particle physics. We then explain how supersymmetry helps us analyze field theories exactly, and what dynamical lessons these solutions…
We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an…
This PhD-thesis reviews matrix string theory and recent developments therein. Emphasis is put on symmetries, interactions and scattering processes in the matrix model. We start with an introduction to matrix string theory and a review of…
Tree-level scattering amplitudes in massless theories not only exhibit a simplicity entirely unexpected from Feynman diagrams, but also an underlying structure remarkably reminiscent of worldsheet theory correlators. These features can be…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as $e^{\ell^2 \Box / 2}$ in the vertices. This nonlocality has hindered the…
A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric…
The topic of cosmic strings provides a bridge between the physics of the very small and the very large. They are predicted by some unified theories of particle interactions. If they exist, they may help to explain some of the largest-scale…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…