Related papers: Fixed Point Structure for 3 dimensional rigid stri…
We develop a geometric framework that unifies several different combinatorial fixed-point theorems related to Tucker's lemma and Sperner's lemma, showing them to be different geometric manifestations of the same topological phenomena. In…
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
A linearly constrained framework in $\mathbb{R}^d$ is a point configuration together with a system of constraints which fixes the distances between some pairs of points and additionally restricts some of the points to lie in given affine…
In this article, we present a new type of fixed point for single valed mapping in a $G$-complete $G$-metric space.
In this thesis time-dependent configurations are studied in the formalism of first-quantized string. These configurations are exact: solutions of the corresponding two-dimensional conformal field theory can be found. We can compute…
Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic…
We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a…
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only…
We analyze brane configurations corresponding to non-trivial six dimensional fixed points. Several results previously obtained from a pure field theoretical analysis are rederived in the brane language.
A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an…
We discuss type II and type I branes at general ADE type orbifold singularities. We show that there are new phases of type I or heterotic string theory in six dimensions, involving extra tensor multiplets, which arise when small instantons…
The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.
In this review article, we review the recent developments in constructing string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include: (a) free…
We study the 6d $\mathcal{N}=(1,0)$ superconformal field theory with smallest non-Higgsable gauge symmetry $SU(3)$. In particular, we propose new 2d gauge theory descriptions of its self-dual strings in the tensor branch. We use our gauge…
In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative gauge theories for open…
We establish three major fixed-point theorems for functions satisfying an odd power type contractive condition in G-metric spaces. We first consider the case of a single mapping, followed by that of a triplet of mappings and we conclude by…
Quantum theory of 2d gravity for $c>1$ is examined as a non-critical string theory by taking account of the loop-correction of open strings whose end points are on the 2d world surface of the closed string. This loop-correction leads to a…
Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially…
The compactness of the closed string in the classical Type II string theory reveals the duality, whereas the compactness of the open string reveals that the end of the string is on the hypersurface which satisfies the Dirichlet boundary…
We introduce and study a new type of mappings in metric spaces termed $n$-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily…