Related papers: Two Lectures on D-Geometry and Noncommutative Geom…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
We solve the worldsheet theory describing the near-horizon dynamics of a D-string in the presence of a very large number N of D5-branes. The model is pre-geometric in the sense that the near-horizon worldsheet Lagrangian does not have…
We discuss the general theory of D-branes on Calabi-Yaus, recent results from the theory of boundary states, and new results on the spectrum of branes on the quintic CY. (Contribution to the proceedings of Strings '99 in Potsdam, Germany.)
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
Much has been learned about string theory over the last few years by studying properties of cycles and branes in a given background geometry. Here we discuss three situations (quantum volume, attractor flows/D-brane stability, and dynamical…
We propose a formulation of d-dimensional SU(N) Yang-Mills theories on a d+2-dimensional space with the extra two dimensions forming a surface with non-commutative geometry. This equivalence is valid in any finite order in the 1/N…
This is a summary of a series of papers hep-th/9910263,0005283,0010066 written with B. Chen, T. Matsuo and K. Murakami on a p-p', (p<p^{\prime}) open string with B_{ij} field, which has led us to the explicit identification of the Dp-brane…
A study of the relation between topology change, energy and Lie algebra representations for fuzzy geometry in connection to $M$-theory is presented. We encounter two different types of topology change, related to the different features of…
In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1)…
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher…
In these lectures we review how some of the recent developments in string theory are closely related to generic properties of supersymmetry. Lectures given at the Nato Advanced Study Institute on "Strings, Branes and Dualities", Cargese,…
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string…
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called…
This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic…
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to…
In this paper, we study a new matrix theory based on non-BPS D-instantons in type IIA string theory and D-instanton - anti D-instanton system in type IIB string theory, which we call K-matrix theory. The theory correctly incorporates the…