Related papers: Strings, paths, and standard tableaux
We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark-Sacker bifurcation giving rise to an attracting invariant…
In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
The Abelian Sandpile generates complex and beautiful patterns and seems to display allometry. On the plane, beyond patches, patterns periodic in both dimensions, we remark the presence of structures periodic in one dimension, that we call…
Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review,…
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the…
A poset on a certain class of partitions known as k-shapes was recently introduced to provide a combinatorial rule for the expansion of a (k-1)-Schur functions into k-Schur functions at t=1. The main ingredient in this construction was a…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in…
The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously as one changes the vacuum on the Coulomb branch of gauge theories with extended supersymmetry in four dimensions. We show that…
Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection…
At the classical level we study open bosonic strings. A generic description of string self-interactions localized at string ends is given. Self-interactions are characterized by two dimensionless coupling constants. The model is rewritten…
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients…
We introduce network science as a framework for studying the string landscape. Two large networks of string geometries are constructed, where nodes are extra-dimensional six-manifolds and edges represent topological transitions between…
In string theory the coupling parameters are functions of moduli fields. The actual values of the coupling constants are then dynamically determined through the vacuum expextation values of these fields. We review the attempts to connect…
We analyze a class of dual pairs of heterotic and type I models based on freely-acting $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifolds in four dimensions. Using the adiabatic argument, it is possible to calculate non-perturbative contributions…
We argue that moduli in the adjoint representation of the standard- model gauge group are a natural feature of superstring models, and that they can account for the apparent discrepancy between the string and unification scales.
We present combinatorial bijections and identities between certain skew Young tableaux, Dyck paths, triangulations, and dissections.
The equivalence of quantum field theory and string theory as exemplified by the AdS/CFT correspondence is explored from the point of view of lightcone quantization. On the string side we discuss the lightcone version of the static string…
Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…