Related papers: Big Numbers in String Theory
Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk. Since in three or more dimensions such walks are transient this approach necessarily…
String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
The past year has seen enormous progress in string theory. It has become clear that all of the different string theories are different limits of a single theory. Moreover, in certain limits, one obtains a new, eleven-dimensional structure…
In the first part of this paper I give an elementary overview about some number sequences which count various sorts of lattice paths in strips along the x-axis and compute their generating functions in terms of Fibonacci and Lucas…
String theory is the most promising candidate theory for a unified description of all fundamental forces exist in the nature. It provides a mathematical framework that combine quantum theory with Einstein's general theory of relativity. But…
The realization that string theory gives rise to a huge landscape of vacuum solutions has recently prompted a statistical approach towards extracting phenomenological predictions from string theory. Unfortunately, for most classes of string…
Much of the recent progress in String Theory can be traced to a precise strategy: a careful study of the few models known since the beginnings of the subject, and the abstraction from them of basic properties that one would like to demand…
We consider the concatenation of $t$ uniformly random perfect matchings on $2n$ vertices, where the operation of concatenation is inspired by the multiplication of generators of the Brauer algebra $\mathfrak{B}_n(\delta)$. For the resulting…
We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to…
Good statistics for measuring large-scale structure in the Universe must be able to distinguish between different models of structure formation. In this paper, two and three dimensional ``counts in cell" statistics and a new ``discrete…
A discrete string theory --a theory of embeddings from ${\bf Z}\times {\bf Z}_C\to {\bf R}^D$, where $C$ is the number of components of the string-- is explored. The closure of the algebra of constraints (`${\bf Z}_C$-Virasoro algebra') is…
This paper concerns the number of lattice points in a circle.
What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman…
I review some of the things we have learned about large N gauge theories (and QCD at N=oo) from lattice calculations in recent years. I point to some open problems.
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important…
These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures…