Related papers: Two Lectures on D-Geometry and Noncommutative Geom…
We study $D$-dimensional $p$-brane Galilean geometries via the intrinsic torsion of their adapted connections. These non-Lorentzian geometries are examples of $G$-structures whose characteristic tensors consist of two degenerate ``metrics''…
In this talk we discuss the need to introduce a string theory in order to obtain a consistent quantum theory of gravity unified with gauge interactions. We then discuss some basic properties of string theory and the origin and the…
This thesis is devoted to the construction and study of D-branes in some curved space-times in string theory. On the one hand, those D-branes are described geometrically as submanifolds subject to Born-Infeld effective dynamics. On the…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding…
We consider open strings ending on D-branes in the presence of constant metric, G, antisymmetric tensor, B and gauge field, A. The Hamiltonian is manifestly invariant under a global noncompact group; strikingly similar to toroidally…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
Non-geometric frames in string theory are related to the geometric ones by certain local O(D,D) transformations, the so-called $\beta$-transforms. For each such transformation, we show that there exists both a natural field redefinition of…
We review some recent results on the extension of the gauge/gravity correspondence to include matter in the fundamental representation by adding D-branes to the supergravity backgrounds. Working in the quenched approximation, in which the…
We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry.
In this set of lectures various properties of D-branes are discussed. After reviewing the basics, we discuss unstable D-brane/anti-D-brane systems, a subject pioneered by Sen. Following him, we discuss the construction of the non-BPS…
We study D-branes on three-dimensional orbifold backgrounds that admit topologically distinct resolutions differing by flop transitions. We show that these distinct phases are part of the vacuum moduli space of the super Yang-Mills gauge…
In these notes we review aspects of semi-realistic particle physics from the point of view of type II orientifold compactifications. We discuss the appearance of gauge theories on spacetime filling D-branes which wrap non-trivial cycles in…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
We perform the consistent quantization of open string D-brane in non-constant NS-NS closed string B field background by directly imposing the worldsheet conformal symmetry. In addition to the previous noncommutative D-brane coordinates…
Stimulated by the importance of noncommutative geometry in recent developments in string theory, D-branes and integrable systems, one intends in this work to present a new insight towards adapting the famous idea of Zeeman effect to…
We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a…
We study the new ``gauge'' theories in 5+1 dimensions, and their non-commutative generalizations. We argue that the $\theta$-term and the non-commutative torus parameters appear on an equal footing in the non-critical string theories which…
Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the…
This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic…