7,839 research outputs found
N=2 structures in all string theories
The BRST cohomology of any topological conformal field theory admits the
structure of a Batalin--Vilkovisky algebra, and string theories are no
exception. Let us say that two topological conformal field theories are
``cohomologically equivalent'' if their BRST cohomologies are isomorphic as
Batalin--Vilkovisky algebras. What we show in this paper is that any string
theory (regardless of the matter background) is cohomologically equivalent to
some twisted N=2 superconformal field theory. We discuss three string theories
in detail: the bosonic string, the NSR string and the W_3 string. In each case
the way the cohomological equivalence is constructed can be understood as
coupling the topological conformal field theory to topological gravity. These
results lend further supporting evidence to the conjecture that _any_
topological conformal field theory is cohomologically equivalent to some
topologically twisted N=2 superconformal field theory. We end the paper with
some comments on different notions of equivalence for topological conformal
field theories and this leads to an improved conjecture.Comment: 23 pages (12 physical pages), .dvi.uu (+ some hyperlinks
Algorithmic aspects of branched coverings
This is the announcement, and the long summary, of a series of articles on
the algorithmic study of Thurston maps. We describe branched coverings of the
sphere in terms of group-theoretical objects called bisets, and develop a
theory of decompositions of bisets.
We introduce a canonical "Levy" decomposition of an arbitrary Thurston map
into homeomorphisms, metrically-expanding maps and maps doubly covered by torus
endomorphisms. The homeomorphisms decompose themselves into finite-order and
pseudo-Anosov maps, and the expanding maps decompose themselves into rational
maps.
As an outcome, we prove that it is decidable when two Thurston maps are
equivalent. We also show that the decompositions above are computable, both in
theory and in practice.Comment: 60-page announcement of 5-part text, to apper in Ann. Fac. Sci.
Toulouse. Minor typos corrected, and major rewrite of section 7.8, which was
studying a different map than claime
Identification of domain walls in coarsening systems at finite temperature
Recently B. Derrida [Phys. Rev. E 55, 3705 (1997)] introduced a numerical
technique that allows one to measure the fraction of persistent spins in a
coarsening nonequilibrium system at finite temperature. In the present work we
extend this method in a way that domain walls can be clearly identified. To
this end we consider three replicas instead of two. As an application we
measure the surface area of coarsening domains in the two-dimensional Ising
model at finite temperature. We also discuss the question to what extent the
results depend on the algorithmic implementation.Comment: 8 pages, revtex, including 6 encapsulated postscript figures, dynamic
exponent correcte
Kolmogorov Complexity of Categories
Kolmogorov complexity theory is used to tell what the algorithmic
informational content of a string is. It is defined as the length of the
shortest program that describes the string. We present a programming language
that can be used to describe categories, functors, and natural transformations.
With this in hand, we define the informational content of these categorical
structures as the shortest program that describes such structures. Some basic
consequences of our definition are presented including the fact that equivalent
categories have equal Kolmogorov complexity. We also prove different theorems
about what can and cannot be described by our programming language.Comment: 16 page
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