Related papers: A Finite Landscape?
This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions,…
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in…
The solution term by term to the scattering of all consistent string theories is given. The moduli space of M-theory is derived and connects the various string theories. The solutions contain both the perturbative and non-perturbative…
It has been claimed that the string landscape predicts an open universe, with negative curvature. The prediction is a consequence of a large number of metastable string vacua, and the properties of the Coleman--De Luccia instanton which…
We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then…
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
In this letter we show that vacuum string field theory contains exact solutions that can be interpreted as macroscopic fundamental strings. They are formed by a condensate of infinitely many completely space-localized solutions (D0-branes).
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We discuss some basic aspects of effective field theory applied to supergravity theories which arise in the low-energy limit of string theory. Our discussion is particularly relevant to the effective field theories of no-scale…
We argue for finiteness of flux vacua around type IIB CY singularities by computing their gauge theory duals. This leads us to propose a geometric transition where the compact 3-cycles support both RR and NS flux, while the open string side…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given…
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.
It is argued that string theory may pose new conceptual issues for the history and philosophy of science.
We show that the $N=2$ superstrings may be viewed as a special class of the $N=4$ superstrings and demonstrate their equivalence. This allows us to realize all known string theories based on linear algebras and with $N<4$ supersymmetries as…
In this paper we describe ideas about the string landscape, and how to relate it to the physics of the Standard Model of particle physics. First, we give a short status report about heterotic string compactifications. Then we focus on the…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric string vacua fills out a ``landscape'' whose features are largely unknown. It is then hoped that progress in…
We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular…