Related papers: On Orbifolds with Discrete Torsion
In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic…
We study geometric properties of linear strata of uni-singular curves. The singularities of closures of the strata are resolved and the resolutions are represent as projective bundles. This enables to study their geometry. In particular we…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
The compactification of the heterotic string on six-dimensional orbifolds is reviewed. Some important technical aspects of their construction are clarified and new parameters, called generalized discrete torsion, are introduced and related…
We use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds. For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations,…
We study topological strings on non-commutative resolutions of singular Calabi-Yau threefolds that are double covers of $\mathbb{P}^3$, ramified over determinantal octic surfaces. Using conifold transitions to complete intersections in…
It is shown using a space-time curvature classification and decomposition that for certain holonomy types of a space-time, proper projective vector fields cannot exist. Existence is confirmed, by example, for the remaining holonomy types.…
Cohen and Glashow argued that very special conformal field theories of a particular kind (i.e. with HOM(2) or SIM(2) invariance) cannot be constructed within the framework of local field theories. We, however, show examples of local…
Constraints on the geometries of static spherically symmetric black holes are obtained by requiring that the spacetime curvature be analytic at the event horizon. Further constraints are obtained by requiring that the semiclassical trace…
This thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. By resolving the orbifold singularities via blow-ups, one arrives at a smooth Calabi-Yau manifold. The systematic method to do so is…
Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior…
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…
We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give…
Recent progress on the complete set of solutions of two dimensional classical string theory in any curved spacetime is reviewed. When the curvature is smooth the string solutions are deformed folded string solutions as compared to flat…
The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue…
The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms…
We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the dynamics of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing…
We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in…
We review the applications of mirror symmetry to the study of the moduli spaces of two-dimensional conformal field theories with $N{=}(2,2)$ supersymmetry, particularly those constructed from Calabi--Yau manifolds. (Lecture delivered at the…