Related papers: Minimum Distances in Non-Trivial String Target Spa…
String theory, as a theory containing quantum gravity, is usually thought to require more dimensions of spacetime than the usual 3+1. Here I argue on physical grounds that needing extra dimensions for strings may well be an artefact of…
We consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional…
The Fermat-Steiner problem consists in finding all points in a metric space $Y$ such that the sum of distances from each of them to the points from some fixed finite subset of $Y$ is minimal. This problem is investigated for the metric…
In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R^{3} which are minimal. In fact, such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the…
A geometrical approach in the non-symmetric connection framework is employed to examine the issue of higher order $\alpha'$ corrections to D=10 type IIB superstring backgrounds with a covariantly constant null Killing isometry and non-zero…
We show how one can get solitonic strings in a six-dimensional (2,0) supersymmetric theory by incorporating a nonlinear interaction term. We derive a zero force condition between parallel strings, and compute a metric on a moduli space…
We use string duality to describe instanton induced spontaneous supersymmetry breaking in string compactifications with additional background fields. Dynamical supersymmetry breaking by space-time instantons in the heterotic string theory…
The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
If $X$ and $Y$ are a mirror pair of Calabi--Yau threefolds, mirror symmetry should extend to an isomorphism between the type IIA string theory compactified on $X$ and the type IIB string theory compactified on $Y$, with all nonperturbative…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity…
If there is a single underlying "theory of everything" which in some limits of its "moduli space" reduces to the five weakly coupled string theories in 10D, and 11D SUGRA, then it is possible that all six of them have some common domain of…
The properties of cosmic strings have been investigated in detail for their implications in early-universe cosmology. Although many variations of the basic structure have been discovered, with implications for both the microscopic and…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…
We consider the minimum distance projection in the $L_2$-norm from an arbitrary point in an $n$-dimensional, Euclidian space onto the canonical simplex. It is shown that this problem reduces to a univariate problem that can be solved by a…
In this review I discuss some basic aspects of non-perturbative string theory. The topics include test of duality symmetries based on the analysis of the low energy effective action and the spectrum of BPS states, relationship between…
The space of four dimensional string and $M$ theory vacua with non-Abelian gauge symmetry, chiral fermions and unbroken supersymmetry beyond the electroweak scale appears to be a disconnected space whose different components represent…