Related papers: Measuring Small Distances in N=2 Sigma Models
By employing the symmetries of the underlying conformal field theory, the tree-level K\"ahler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries…
We consider the moduli space of the extremal K\"ahler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can…
We review the geometry of K3 surfaces and then describe this geometry from the point of view of an approximate metric of Gibbons-Hawking form. This metric arises from the M-theory lift of the tree-level supergravity description of type IIA…
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory. Recently, we have…
In this paper we investigate the properties of series of vacua in the string theory landscape. In particular, we study minima to the flux potential in type IIB compactifications on the mirror quintic. Using geometric transitions, we embed…
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
The moduli of N=1 compactifications of IIB string theory can be stabilized by a combination of fluxes (which freeze complex structure moduli and the dilaton) and nonperturbative superpotentials (which freeze Kahler moduli), typically…
We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for…
We study the hypermultiplet moduli space of the type II string compactified on a Calabi-Yau space $\bX$. We do this by using IIA/IIB duality in a compactification of the same theory on $\bX\times \bS ^1$ and by using recent results on three…
We introduce a method of using the a dual type IIA string to compute alpha'-corrections to the moduli space of heterotic string compactifications. In particular we study the hypermultiplet moduli space of a heterotic string on a K3 surface.…
Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These…
The paper is devoted to an algebraic analogue of a geometric approach to the classical notion of complex dilatation suggested in the paper arXiv:1701.06259 [math.CV] by the author. At the same time it provides an invariant version of this…
Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion…
In this work we investigate the moduli stabilisation problem and the requirements for de Sitter vacua within the framework of type IIB string theory. Using perturbative effects arising from the various sources such as $\alpha^\prime$…
We study the spectrum, couplings and cosmological and astrophysical implications of the moduli fields for the class of Calabi-Yau IIB string compactifications for which moduli stabilisation leads to an exponentially large volume V ~ 10^{15}…
We analyse a new ${\cal N}=1$ string tree level correction at ${\cal O}(\alpha'^2)$ to the K\"ahler potential of the volume moduli of type IIB Calabi-Yau flux compactification found recently by Grimm, Savelli and…
We give some simple examples of mirror Calabi-Yau fourfolds in Type II string theory. These are realised as toroidal orbifolds. Motivated by the Strominger, Yau, Zaslow argument we give explicitly the mirror transformation which maps Type…
We study the statistics of the metric on K\"ahler moduli space in compactifications of string theory on Calabi-Yau hypersurfaces in toric varieties. We find striking hierarchies in the eigenvalues of the metric and of the Riemann curvature…
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…
We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective…