4,325 research outputs found
Logic and operator algebras
The most recent wave of applications of logic to operator algebras is a young
and rapidly developing field. This is a snapshot of the current state of the
art.Comment: A minor chang
Symmetry breaking boundaries II. More structures; examples
Various structural properties of the space of symmetry breaking boundary
conditions that preserve an orbifold subalgebra are established. To each such
boundary condition we associate its automorphism type. It is shown that
correlation functions in the presence of such boundary conditions are
expressible in terms of twisted boundary blocks which obey twisted Ward
identities. The subset of boundary conditions that share the same automorphism
type is controlled by a classifying algebra, whose structure constants are
shown to be traces on spaces of chiral blocks. T-duality on boundary conditions
is not a one-to-one map in general. These structures are illustrated in a
number of examples. Several applications, including the construction of non-BPS
boundary conditions in string theory, are exhibited.Comment: 51 pages, LaTeX2
CFT fusion rules, DHR gauge groups, and CAR algebras
It is demonstrated that several series of conformal field theories, while
satisfying braid group statistics, can still be described in the conventional
setting of the DHR theory, i.e. their superselection structure can be
understood in terms of a compact DHR gauge group. Besides theories with only
simple sectors, these include (the untwisted part of) c=1 orbifold theories and
level two so(N) WZW theories. We also analyze the relation between these models
and theories of complex free fermions.Comment: 22 pages, LaTeX2
CPT Groups of Spinor Fields in de Sitter and Anti-de Sitter Spaces
groups for spinor fields in de Sitter and anti-de Sitter spaces are
defined in the framework of automorphism groups of Clifford algebras. It is
shown that de Sitter spaces with mutually opposite signatures correspond to
Clifford algebras with different algebraic structure that induces an essential
difference of groups associated with these spaces. groups for
charged particles are considered with respect to phase factors on the various
spinor spaces related with real subalgebras of the simple Clifford algebra over
the complex field (Dirac algebra). It is shown that groups for neutral
particles which admit particle-antiparticle interchange and groups for
truly neutral particles are described within semisimple Clifford algebras with
quaternionic and real division rings, respectively. A difference between
bosonic and fermionic groups is discussed.Comment: 31 pages. arXiv admin note: text overlap with arXiv:math-ph/0405040,
arXiv:math-ph/0203059, arXiv:math-ph/030603
Symmetry breaking boundary conditions and WZW orbifolds
Symmetry breaking boundary conditions for WZW theories are discussed. We
derive explicit formulae for the reflection coefficients in the presence of
boundary conditions that preserve only an orbifold subalgebra with respect to
an involutive automorphism of the chiral algebra. The characters and modular
transformations of the corresponding orbifold theories are computed. Both inner
and outer automorphisms are treated.Comment: 39 pages, LaTeX2
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