Related papers: A solution manual for Polchinski's "String Theory"
This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of ST within the broader context of six decades of failed attempts…
We address the problem of counting the number of strings in a collection where a given pattern appears, which has applications in information retrieval and data mining. Existing solutions are in a theoretical stage. We implement these…
String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than thirty years of its existence, it does not make any empirically testable predictions, and it…
We review the current status of the singularity problem in string theory for non-experts. After the problem is discussed from the point of view of supergravity, we discuss classic examples and recent examples of singularity resolution in…
Let E_n={x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}}. For each integer n \geq 13, J. Browkin defined a system B_n \subseteq E_n which has exactly b_n solutions in integers x_1,...,x_n, where b_n \in N\{0} and the sequence…
We review various aspects of classical solutions in string theories. Emphasis is placed on their supersymmetry properties, their special roles in string dualities and microscopic interpretations. Topics include black hole solutions in…
We find new classes of {\it exact} string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as {\it multi-string} solutions, in terms…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
An infinite number of distinct $d=1$ matrix models reproduce the perturbation theory of $d=2$ string theory. Due to constraints of causality, however, we argue that none of the existing constructions gives a consistent nonperturbative…
String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored…
1. The 2-Toda lattice and its generic symmetries 2. A Larger class of symmetries for special initial conditions 3. Borel decomposition of Moment matrices, tau-functions and string-orthogonal polynomials 4. From string-orthogonal Polynomials…
We give self-contained presentation of results related to the Kadison-Singer problem, which was recently solved by Marcus, Spielman, and Srivastava. This problem connects with unusually large number of areas including: operator algebras…
In bosonic string theory, the solutions to the string equations of motion may be expressed as two-dimensional manifolds in a relativistic spacetime. We develop MATLAB software for the generation of open and closed string solutions and for…
Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…
A polemical article evaluating string theory from the point of view of a quantum field theorist working in a mathematics department. Comments to the author are encouraged.
If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all non-gravitational physics: the Standard Model. But despite this monumental achievement…
We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
We provide infinitely many solutions of a Dirichlet problem on balls.
We give three different computations of the total number of runs of length $i$ in binary $n$-strings, and we discuss the connection of this problem with the compositions of $n$.