Related papers: String Theory and non-Riemannian Geometry

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such…

Taking $\mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative…

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which…

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a…

Nonrelativistic string theory is described by a sigma model with a relativistic worldsheet and a nonrelativistic target spacetime geometry, that is called string Newton-Cartan geometry. In this paper we obtain string Newton-Cartan geometry…

We perform canonical quantization of the open Neveu-Schwarz-Ramond (NSR) superstrings in the background of a D-brane with the NS B-field. If we choose the mixed boundary condition as a primary constraint, it generates a set of secondary…

We review recent developments on nonrelativistic string theory. In flat spacetime, the theory is defined by a two-dimensional relativistic quantum field theory with nonrelativistic global symmetries acting on the worldsheet fields. This…

Double Field Theory (DFT) has emerged as a comprehensive framework for gravity, presenting a testable and robust alternative to General Relativity (GR), rooted in the $\mathbf{O}(D,D)$ symmetry principle of string theory. These lecture…

Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The…

The recently discovered $O(d,d)$ symmetry of the space of slowly varying cosmological string vacua in $d+1$ dimensions is shown to be preserved in the presence of bulk string matter. The existence of $O(d,d)$ conserved currents allows all…

It has been known for a while that the effective geometrical description of compactified strings on $d$-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized…

Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first…

A new framework is found for the compactification of supersymmetric string theory. It is shown that the massless spectra of Calabi--Yau manifolds of complex dimension $D_{crit}$ can be derived from noncritical manifolds of complex dimension…

In this Thesis we investigate properties of stability, rigidity and unitarity of the string landscape in ten and lower dimensions. The dissertation explores these aspects by intertwining a detailed analysis of string vacua, with and without…

The nonrelativistic bosonic string theory in a curved manifold is formulated here using gauging of symmetry approach ( Galilean Gauge theory ) . The corresponding model in flat space has some global symmetries . By localizing these…

An $O(d,d)$ symmetry of the manifold of string vacua that do not depend on $d$ (out of $D$) space-time coordinates has been recently identified. Here we write down, for $d=D-1$, the low energy equations of motion and their general solution…

A recently introduced framework for the compactification of supersymmetric string theory involving noncritical manifolds of complex dimension $2k+D_{crit}$, $k\geq 1$, is reviewed. These higher dimensional manifolds are spaces with…

In the covariant-gauge two-dimensional quantum gravity, various derivations of the critical dimension D=26 of the bosonic string are critically reviewed, and their interrelations are clarified. It is shown that the string theory is not…

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct {\sl ab initio} quantized bosonic string theory with…

Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and…