Related papers: String structures and loop spaces
We discuss the role played by logarithmic structures in the theory of moduli.
We use our model of the small scale structure on cosmic strings to develop further the result of Siemens, Olum, and Vilenkin that the gravitational radiation length scale on cosmic strings is smaller than the previously assumed $\Gamma G\mu…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
Some points concerning the relation of strings to interfaces in statistical systems are discussed.
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has…
A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauge transformations in the…
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
We investigate the most general phase space of configurations, consisting of all possible ways of assigning elementary attributes, ``energies'', to elementary positions, ``cells''. We discuss how this space possesses structures that can be…
In this talk, based on work done in collaboration with G. Landi and R.J Szabo, I will review how string theory can be considered as a noncommutative geometry based on an algebra of vertex operators. The spectral triple of strings is…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We study cosmic strings in the complex symmetron model, a scalar-tensor theory with a spontaneously broken local $U(1)$ symmetry in low matter density regions. Using numerical simulations, we show that these strings preferentially attach to…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
In this paper we study the string topology (\'a la Chas-Sullivan) of an orbifold. We define the string homology ring product at the level of the free loop space of the classifying space of an orbifold. We study its properties (introducing…
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…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…