Related papers: The measure in three dimensional Nambu-Goto string…
An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…
We introduce bridge trisections of knotted surfaces in the four-sphere. This description is inspired by the work of Gay and Kirby on trisections of four-manifolds and extends the classical concept of bridge splittings of links in the…
We consider type IIA/B strings in two-dimensions and their projection with respect to the nilpotent space-time supercharge. Based on the ground ring structure, we propose a duality between perturbed type II strings and the topological…
Various string theory realizations of three-dimensional gauge theories relate them to gravitational instantons, Nahm equations and monopoles. We use this correspondence to model self-dual gravitational instantons of $D_k$-type as moduli…
The dynamics of a vortex string, which describes the Nambu-Goldtone modes of the spontaneous breakdown of the target space D=4, N=1 supersymmetry and internal $U(1)_R$ symmetry to the world sheet ISO(1,1) symmetry, is constructed by using…
The three string vertex for Type IIB superstrings in a maximally supersymmetric plane-wave background can be constructed in a light-cone gauge string field theory formalism. The detailed formula contains certain Neumann coefficients, which…
Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
We prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric, and use this to give a complete classification of such surfaces for any given value of the mean curvature.
Entropy is a natural geometric quantity measuring the complexity of a surface embedded in $\mathbb{R}^3$. For dynamical reasons relating to mean curvature flow, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
In this paper we solve the non-linear Lagrange's equations for the Nambu-Goto closed bosonic string. We show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the…
We construct an invariant measure $\mu$ for the Surface Quasi-Geostrophic (SQG) equation and show that almost all functions in the support of $\mu$ are initial conditions of global, unique solutions of SQG, that depend continuously on the…
We give simple string theory embeddings of several recently introduced dualities between 2+1-dimensional Chern-Simons matter theories using probe brane holography. Our construction is reliable in the limit of a large number of colors $N$…
It is well known that a straight Nambu-Goto string is an exact solution of the equations of motion when its end moves in a circular orbit. In this paper we investigate the shape of a confining relativistic string for a general motion of its…
Our purpose is to offer a logical analysis of the system of units and to explore possible paths towards a consistent and unified system with an original perspective. The path taken here builds on the fact that, thanks to optical or…
We study the effective string description of space-like Polyakov loop correlators at finite temperature with the goal of describing the behaviour of the space--like string tension in the vicinity of the deconfinement transition. To this end…
Assouad-Nagata dimension addresses both large and small scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space $M$ is a minor-closed metric if there exists an (edge-)weighted graph $G$…