Related papers: Virtual strings
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
We classify closed curves on a once-punctured torus with a single self-intersection from a combinatorial perspective. We determine the number of closed curves with given word-length and with zero, one, and arbitrary self-intersections.
String graphs, that is, intersection graphs of curves in the plane, have been studied since the 1960s. We provide an expository presentation of several results, including very recent ones: some string graphs require an exponential number of…
The unique, conical spacetime created by cosmic strings brings about distinctive gravitational lensing phenomena. The variety of these distinctive phenomena is increased when the strings have non-trivial mutual interactions. In particular,…
A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
We survey recent progress in understanding the relation of string theory to quantum chromodynamics, focusing on holographic models of gauge theories similar to QCD and applications to heavy-ion collisions.
We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…
In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…
String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, in the bosonic closed sector of string geometry theory, we completely identify the perturbative vacua, which include…
We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both…
Vortons are closed loops of superconducting strings carrying current and charge. A formalism has been developed to study vortons in terms of an elastic string approximation, but its implementation requires knowledge of the unknown equation…
I present a class of objects called gravitational strings (GS) for their similarity to the conventional cosmic strings: even though the former are just singularities in flat spacetime, both varieties are equally "realistic", they may play…
Special kind of closed strings is considered. It is shown that these closed strings behave as two (an even number of) open strings at the classical level and one open string at the quantum level. They contain massless vector field in their…
In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is that this may lead to an algebraic formulation of string…
String Field Theory is a formulation of String Theory as a Quantum Field Theory in target space. It allows to tame the infrared divergences of String Theory and to approach its non-perturbative structure and background independence. This…
We construct complete sets of (open and closed string) covariant coherent state and mass eigenstate vertex operators in bosonic string theory. This construction can be used to study the evolution of fundamental cosmic strings as predicted…
In this paper we will discuss how cosmic strings can be used to bridge the gap between the local geometry of our spacetime model and the global topology. The primary tool is the theory of foliations and surfaces, and together with…
I consider a three-dimensional string theory whose action, besides the standard area term, contains one of the form $\int_{\Sigma} \epsilon_{\mu\nu\sigma} X^{\mu} d X^{\nu} \wedge d X^{\sigma}$. In the case of closed strings this extra term…
I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods.