Related papers: A solution manual for Polchinski's "String Theory"
A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue…
These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same authors (along with Spielman) which appeared at the 2014 ICM. In…
The cosmological constant and electroweak hierarchy problem have been a great inspiration for research. Nevertheless, the resolution of these two naturalness problems remains mysterious from the perspective of a low-energy effective field…
Consider the $n$th degree polynomial equation, $X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices. If this equation has more than ${2n \choose 2}$ solutions, then it has infinitely many solutions. We show here that…
We review some exact solitonic solutions of string theory with higher-membrane structure. These include an axionic instanton solution of bosonic string theory as well as multi-instanton and multimonopole solutions of heterotic string…
The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.
In this paper we count the numbers of real and complex solutions to Bethe constraints in the two particle sector of the XXZ model. We find exact number of exceptions to the string conjecture and total number of solutions which is required…
This is an invited contribution to the Special Issue of "Foundations of Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations". I have been asked to assess string theory as an outsider, and to compare it with the…
As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require…
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
This is a survey on the exact complexity of computing the Tutte polynomial. It is the longer 2017 version of Chapter 25 of the CRC Handbook on the Tutte polynomial and related topics, edited by J. Ellis-Monaghan and I. Moffatt, which is due…
We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range (\epsilon \leq |z| \leq1). We explain how rational approximations can be applied to large sparse…
Each researcher should have a full shelf---physical or virtual---of books on writing and editing prose. Though we make no claim to any special degree of expertise, we recently edited a book of complexity theory surveys (Complexity Theory…
The black hole solutions to Einstein's vacuum field equations are also solutions to the equations of motion of the low energy limit of superstring theory. At the same time, string theory boasts a much broader and richer collection of black…
We present a review of the status of $W$ string theories, their physical spectra, and their interactions. (Based on review talks given at the Trieste Spring Workshop, and the Strings 93 meeting at Berkeley, May 1993.)
We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study…
In this paper, we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin combined with some properties of…
These lectures intend to give a pedagogical introduction into some of the developments in string theory during the last years. They include perturbative T-duality and non perturbative S- and U-dualities, their unavoidable demand for…