Related papers: Stringy Geometry and Topology of Orbifolds
Recent developments about the construction of standard $SO(10)$ and $SU(5)$ grand unified theories from 4-dimensional superstrings are presented. Explicit techniques involving higher level affine Lie algebras, for obtaining such stringGUTs…
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.
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct…
This article reviews recent developments in the study of universes with a positive cosmological constant in string theory.
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the…
In this work we provide a self-contained and modern introduction to some of the tools, obstacles and open questions arising in string compactifications. Techniques and current progress are illustrated in the context of smooth heterotic…
The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra…
To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.
The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples.…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of…
A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…
We obtain the spectrum of heterotic strings compactified on orbifolds, focusing on its algebraic structure. Affine Lie algebra provides its current algebra and representations. In particular the twisted spectrum and the Abelian charge are…
Homotopy algebra and its involutive generalisation plays an important role in the construction of string field theory. I will review recent progress in these applications of homotopy algebra and its relation to moduli spaces.
The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each component compactified as a…