16,232 research outputs found
Independence in computable algebra
We give a sufficient condition for an algebraic structure to have a
computable presentation with a computable basis and a computable presentation
with no computable basis. We apply the condition to differentially closed, real
closed, and difference closed fields with the relevant notions of independence.
To cover these classes of structures we introduce a new technique of safe
extensions that was not necessary for the previously known results of this
kind. We will then apply our techniques to derive new corollaries on the number
of computable presentations of these structures. The condition also implies
classical and new results on vector spaces, algebraically closed fields,
torsion-free abelian groups and Archimedean ordered abelian groups.Comment: 24 page
On the worldsheet theories of strings dual to free large N gauge theories
We analyze in detail some properties of the worldsheet of the closed string
theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories
(with adjoint matter fields). We use Gopakumar's prescription to translate the
computation of space-time correlation functions to worldsheet correlation
functions for several classes of Feynman diagrams, by explicit computations of
Strebel differentials. We compute the worldsheet operator product expansion in
several cases and find that it is consistent with general worldsheet conformal
field theory expectations. A peculiar property of the construction is that in
several cases the resulting worldsheet correlation functions are non-vanishing
only on a sub-space of the moduli space (say, for specific relations between
vertex positions). Another strange property we find is that for a conformally
invariant space-time theory, the mapping to the worldsheet does not preserve
the special conformal symmetries, so that the full conformal group is not
realized as a global symmetry on the worldsheet (even though it is, by
construction, a symmetry of all integrated correlation functions).Comment: 60 pages, 17 figures, latex. v2: Added references and a minor
correctio
A cellular topological field theory
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect to composition of cobordisms
Towards a Model Theory for Transseries
The differential field of transseries extends the field of real Laurent
series, and occurs in various context: asymptotic expansions, analytic vector
fields, o-minimal structures, to name a few. We give an overview of the
algebraic and model-theoretic aspects of this differential field, and report on
our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p
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