1,630 research outputs found
A-D-E Classification of Conformal Field Theories
The ADE classification scheme is encountered in many areas of mathematics,
most notably in the study of Lie algebras. Here such a scheme is shown to
describe families of two-dimensional conformal field theories.Comment: 19 pages, 4 figures, 4 tables; review article to appear in
Scholarpedia, http://www.scholarpedia.org
Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
We construct d=4,N=1 orientifolds of Gepner models with just the chiral
spectrum of the standard model. We consider all simple current modular
invariants of c=9 tensor products of N=2 minimal models. For some very specific
tensor combinations, and very specific modular invariants and orientifold
projections, we find a large number of such spectra. We allow for standard
model singlet (dark) matter and non-chiral exotics. The Chan-Paton gauge group
is either U(3) x Sp(2) x U(1) x U(1) or U(3) x U(2) x U(1) x U(1). In many
cases the standard model hypercharge U(1) has no coupling to RR 2-forms and
hence remains massless; in some of those models the B-L gauge boson does
acquire a mass.Comment: 16 pages, LaTeX, minor corrections, references added Link added to
updated and almost complete result
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Topological dualities in the Ising model
We relate two classical dualities in low-dimensional quantum field theory:
Kramers-Wannier duality of the Ising and related lattice models in
dimensions, with electromagnetic duality for finite gauge theories in
dimensions. The relation is mediated by the notion of boundary field theory:
Ising models are boundary theories for pure gauge theory in one dimension
higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t
Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects
the multiplicity of topological boundary states. In the process we describe
lattice theories as (extended) topological field theories with boundaries and
domain walls. This allows us to generalize the duality to non-abelian groups;
finite, semi-simple Hopf algebras; and, in a different direction, to finite
homotopy theories in arbitrary dimension
Topological dualities in the Ising model
We relate two classical dualities in low-dimensional quantum field theory:
Kramers-Wannier duality of the Ising and related lattice models in
dimensions, with electromagnetic duality for finite gauge theories in
dimensions. The relation is mediated by the notion of boundary field theory:
Ising models are boundary theories for pure gauge theory in one dimension
higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t
Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects
the multiplicity of topological boundary states. In the process we describe
lattice theories as (extended) topological field theories with boundaries and
domain walls. This allows us to generalize the duality to non-abelian groups;
finite, semi-simple Hopf algebras; and, in a different direction, to finite
homotopy theories in arbitrary dimension.Comment: 62 pages, 22 figures; v2 adds important reference [S]; v2 has
reworked introduction, additional reference [KS], and minor changes; v4 for
publication in Geometry and Topology has all new figures and a few minor
changes and additional reference
Definable sets of Berkovich curves
In this article, we functorially associate definable sets to -analytic
curves, and definable maps to analytic morphisms between them, for a large
class of -analytic curves. Given a -analytic curve , our association
allows us to have definable versions of several usual notions of Berkovich
analytic geometry such as the branch emanating from a point and the residue
curve at a point of type 2. We also characterize the definable subsets of the
definable counterpart of and show that they satisfy a bijective relation
with the radial subsets of . As an application, we recover (and slightly
extend) results of Temkin concerning the radiality of the set of points with a
given prescribed multiplicity with respect to a morphism of -analytic
curves.
In the case of the analytification of an algebraic curve, our construction
can also be seen as an explicit version of Hrushovski and Loeser's theorem on
iso-definability of curves. However, our approach can also be applied to
strictly -affinoid curves and arbitrary morphisms between them, which are
currently not in the scope of their setting.Comment: 53 pages, 1 figure. v2: Section 7.2 on weakly stable fields added and
other minor changes. Final version. To appear in Journal of the Institute of
Mathematics of Jussie
Analytic cell decomposition and analytic motivic integration
The main results of this paper are a Cell Decomposition Theorem for Henselian
valued fields with analytic structure in an analytic Denef-Pas language, and
its application to analytic motivic integrals and analytic integrals over
\FF_q((t)) of big enough characteristic. To accomplish this, we introduce a
general framework for Henselian valued fields with analytic structure, and
we investigate the structure of analytic functions in one variable, defined on
annuli over . We also prove that, after parameterization, definable analytic
functions are given by terms. The results in this paper pave the way for a
theory of \emph{analytic} motivic integration and \emph{analytic} motivic
constructible functions in the line of R. Cluckers and F. Loeser
[\emph{Fonctions constructible et int\'egration motivic I}, Comptes rendus de
l'Acad\'emie des Sciences, {\bf 339} (2004) 411 - 416]
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