Related papers: Minimum Distances in Non-Trivial String Target Spa…
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…
We describe local Calabi-Yau geometries with two isolated singularities at which systems of D3- and D7-branes are located, leading to chiral sectors corresponding to a semi-realistic visible sector and a hidden sector with dynamical…
Recently a systematic investigation of monoids of sequences of plus-minus weighted zero-sum sequences had been started, which is among others motivated by applications to monoids of norms of algebraic integers. In the current paper these…
We consider dual optimization problems to the fundamental problem of finding the minimum distance from a point to a subspace. We provide a counterexample to a theorem which has appeared in the literature, relating the minimum distance…
Within a Liouville approach to non-critical string theory, we argue for a non-trivial commutation relation between space and time observables, leading to a non-zero space-time uncertainty relation $\delta x \delta t > 0$, which vanishes in…
Starting from a sigma-model for a doubled target-space geometry, we show that the number of target-space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double…
In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance) is investigated. It is easy to construct an example of…
In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
String theory requires additional degrees of freedom to maintain world-sheet reparameterisation invariance at the quantum level. These are often interpreted as extra dimensions, beyond the 4 space-time. I discuss a class of quasi-realistic…
A family of exact conformal field theories is constructed which describe charged black strings in three dimensions. Unlike previous charged black hole or extended black hole solutions in string theory, the low energy spacetime metric has a…
It is argued that every Calabi-Yau manifold $X$ with a mirror $Y$ admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space $Y$. The mirror…
After a brief introduction into the use of Calabi--Yau varieties in string dualities, and the role of toric geometry in that context, we review the classification of toric Calabi-Yau hypersurfaces and present some results on complete…
As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an asymptotically tensionless, weakly coupled string…
In this paper, we consider a specific model, implementing the existence of a fundamental limit distance $L_0$ between (space or time separated) points in spacetime, which in the recent past has exhibited the intriguing feature of having a…
In these introductory notes I explain some basic ideas in string field theory. These include: the concept of a string field, the issue of background independence, the reason why minimal area metrics solve the problem of generating all…
We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…
The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined…
It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are…
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons…