Related papers: String structures and loop spaces
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
Cosmic strings provide a radically different paradigm for the formation of structure to the prevailing inflationary one. They afford some extra technical complications: for example, the calculation of the power spectrum of matter and…
These four lectures, addressed to an audience of graduate students in experimental high energy physics, survey some of the basic concepts in string theory. The purpose is to convey a general sense of what string theory is and what it has…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string…
It is hoped that these lectures will give a point of entry into that vast web of related ideas that go under the name "string theory". I start with a more or less qualitative introduction to gravity as a field theory and sketch how one…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
The geometric properties of spacetimes representing expanding impulsive gravitational waves, propagating on a flat background and generated by snapped cosmic strings, are studied. The construction of the line element is reviewed, and…
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
We briefly review the present status of string theory from the viewpoint of its implications on the short-distance space-time structure and black hole physics. Special emphases are given on two closely related issues in recent developments…
This paper is a review of the relationship between the metric formulation of (2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the geometry, via the theory of geometric…
Using light cone string field theory we derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory. These results extend to strings in a plane wave…
This course is designed to give a mathematically coherent introduction to the classical thory of black holes and also of strings and membranes (which are like the horizon of a black hole in being examples of physical systems based on a…
A string model with dynamical metric and torsion is proposed. The geometry of the string is described by an effective Lagrangian for the scalar and vector fields. The path integral quantization of the string is considered.
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties…
This article briefly summarizes the motivations for -- and recent progress in -- searching for cosmological configurations within string theory, with a focus on how much we might reasonably hope to learn about fundamental physics from…
We discuss the notion of generalised hyperKaehler structure in the context of string theory and discuss examples of this geometry.
An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.