Related papers: Introduction to Differential W-Geometry
The introduction of General Relativity (GR) in 1915 revolutionized our understanding of gravity, but over time, its limitations in explaining phenomena like dark energy, dark matter, and quantum gravity have motivated alternative theories.…
In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe…
The low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric superspace formulation. We show that a previously proposed relaxation of the torsion constraints can indeed…
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of…
The properties of a string-inspired two-dimensional theory of gravity are studied. The post-Newtonian and weak-field approximations, `stellar' structure and cosmological solutions of this theory are developed. Some qualitative similarities…
In these lectures I review the progress made over the last few years in the subject of string and string-inspired phenomenology. I take a practical approach, thereby concentrating more on explicit examples rather than on formal…
(from the talk:) I shall here speak on gravity in (1+1)-dimensional space-time --- lineal gravity. The purpose of studying lower dimensional theories, and specifically lower dimensional gravity, is to gain insight into difficult…
In these lectures we review Generalized Complex Geometry and discuss two main applications to string theory: the description of supersymmetric flux compactifications and the supersymmetric embedding of D-branes. We start by reviewing…
Two solutions of stringy gravity in three and four dimensions which admit interpretation as a black hole and a black string, respectively, are discussed. It is demonstrated that they are exact WZWN nonlinear sigma models to all orders in…
Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for…
Wavefunctionals of three dimensional quantum gravity are extracted from the 3D field theoretic analogs of the four dimensional Donaldson polynomials. Our procedure is generalizable to four and other dimensions. This is a summary of a talk…
I discuss the early developments of string theory with respect to its connection with gauge theory and general relativity from my own perspective. The period covered is mainly from 1969 to 1974, during which I became involved in research on…
We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a…
Continuum and discrete approaches to 2d gravity coupled to $c<1$ matter are reviewed.
The unified theory of string and two-dimensional quantum gravity is considered. The action for two-dimensional gravity is choosen in a well-known induced form and thus gravity posesses it's oun nontrivial dynamics even on the classical…
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
We give a review of some recent developments in the quantisation of $W$-gravity theories. In particular, we discuss the construction of anomaly-free $W_\infty$ and $W_3$ gravities.
We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a…
The structure of differential equations as they appear in special \K\ geometry of $N=2$ supergravity and $(2,2)$ vacua of the heterotic string is summarized. Their use for computing couplings in the low energy effective Lagrangians of…
We study the case in which the five dimensional theory is the transformed Weyl$-$Yang$-$Kaluza$-$Klein gravity. The dimensionally reduced equations of motion are derived by considering an alternative form of the main equation of the theory…