309 research outputs found
Scattering States of Plektons (PARTICLES with Braid Group Statistics) in 2+1 Dimensional Quantum Field Theory
A Haag-Ruelle scattering theory for particles with braid group statistics is
developed, and the arising structure of the Hilbert space of multiparticle
states is analyzed.Comment: 18 pages, LATEX, DAMTP-94-9
Translocality and a Duality Principle in Generally Covariant Quantum Field Theory
It is argued that the formal rules of correspondence between local
observation procedures and observables do not exhaust the entire physical
content of generally covariant quantum field theory. This result is obtained by
expressing the distinguishing features of the local kinematical structure of
quantum field theory in the generally covariant context in terms of a
translocal structure which carries the totality of the nonlocal kinematical
informations in a local region. This gives rise to a duality principle at the
dynamical level which emphasizes the significance of the underlying translocal
structure for modelling a minimal algebra around a given point. We discuss the
emergence of classical properties from this point of view.Comment: 12 pages. To appear in Classical Quantum Gravit
Symmetries of perturbed conformal field theories
The symmetries of perturbed conformal field theories are analysed. We explain
which generators of the chiral algebras of a bulk theory survive a perturbation
by an exactly marginal bulk field. We also study the behaviour of D-branes
under current-current bulk deformations. We find that the branes always
continue to preserve as much symmetry as they possibly can, i.e. as much as is
preserved in the bulk. We illustrate these findings with several examples,
including permutation branes in WZW models and B-type D-branes in Gepner
models.Comment: 30 pages, 3 figures. V2: Small error in eq. (2.14) correcte
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
We present a method of short-distance analysis in quantum field theory that
does not require choosing a renormalization prescription a priori. We set out
from a local net of algebras with associated pointlike quantum fields. The net
has a naturally defined scaling limit in the sense of Buchholz and Verch; we
investigate the effect of this limit on the pointlike fields. Both for the
fields and their operator product expansions, a well-defined limit procedure
can be established. This can always be interpreted in the usual sense of
multiplicative renormalization, where the renormalization factors are
determined by our analysis. We also consider the limits of symmetry actions. In
particular, for suitable limit states, the group of scaling transformations
induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
Braid group statistics implies scattering in three-dimensional local quantum physics
It is shown that particles with braid group statistics (Plektons) in
three-dimensional space-time cannot be free, in a quite elementary sense: They
must exhibit elastic two-particle scattering into every solid angle, and at
every energy. This also implies that for such particles there cannot be any
operators localized in wedge regions which create only single particle states
from the vacuum and which are well-behaved under the space-time translations
(so-called temperate polarization-free generators). These results considerably
strengthen an earlier "NoGo-theorem for 'free' relativistic Anyons".
As a by-product we extend a fact which is well-known in quantum field theory
to the case of topological charges (i.e., charges localized in space-like
cones) in d>3, namely: If there is no elastic two-particle scattering into some
arbitrarily small open solid angle element, then the 2-particle S-matrix is
trivial.Comment: 25 pages, 4 figures. Comment on model-building added in the
introductio
Level-rank duality of untwisted and twisted D-branes of the so(N)_K WZW model
We analyze the level-rank duality of untwisted and epsilon-twisted D-branes
of the so(N)_K WZW model. Untwisted D-branes of so(N)_K are characterized by
integrable tensor and spinor representations of so(N)_K. Level-rank duality
maps untwisted so(N)_K D-branes corresponding to (equivalence classes of)
tensor representations onto those of so(K)_N. The epsilon-twisted D-branes of
so(2n)_2k are characterized by (a subset of) integrable tensor and spinor
representations of so(2n-1)_2k+1. Level-rank duality maps spinor
epsilon-twisted so(2n)_2k D-branes onto those of so(2k)_2n. For both untwisted
and epsilon-twisted D-branes, we prove that the spectrum of an open string
ending on these D-branes is isomorphic to the spectrum of an open string ending
on the level-rank-dual D-branes.Comment: 18 page
Presentations of Wess-Zumino-Witten Fusion Rings
The fusion rings of Wess-Zumino-Witten models are re-examined. Attention is
drawn to the difference between fusion rings over Z (which are often of greater
importance in applications) and fusion algebras over C. Complete proofs are
given characterising the fusion algebras (over C) of the SU(r+1) and Sp(2r)
models in terms of the fusion potentials, and it is shown that the analagous
potentials cannot describe the fusion algebras of the other models. This
explains why no other representation-theoretic fusion potentials have been
found.
Instead, explicit generators are then constructed for general WZW fusion
rings (over Z). The Jacobi-Trudy identity and its Sp(2r) analogue are used to
derive the known fusion potentials. This formalism is then extended to the WZW
models over the spin groups of odd rank, and explicit presentations of the
corresponding fusion rings are given. The analogues of the Jacobi-Trudy
identity for the spinor representations (for all ranks) are derived for this
purpose, and may be of independent interest.Comment: 32 pages, 3 figures, added references, minor additions to text. To be
published in Rev. Math. Phy
How to remove the boundary in CFT - an operator algebraic procedure
The relation between two-dimensional conformal quantum field theories with
and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte
D-branes on a Deformation of SU(2)
We discuss D-branes on a line of conformal field theories connected by an
exact marginal deformation. The line contains an SU(2) WZW model and two
mutually T-dual SU(2)/U(1) cosets times a free boson. We find the D-branes
preserving a U(1) isometry, an F-flux quantization condition and conformal
invariance. Away from the SU(2) point a U(1) times U(1) symmetry is broken to
U(1) times Z_k, i.e. continuous rotations of branes are accompanied by
rotations along the branes. Requiring decoupling of the cosets from the free
boson at the endpoints of the deformation breaks the continuous rotation of
branes to Z_k. At the SU(2) point the full U(1) times U(1) symmetry is
restored. This suggests the occurrence of phase transitions for branes at
angles in the coset model, at a semiclassical level. We also discuss briefly
the orientifold planes along the deformation line.Comment: 19 pages, latex, 5 figures, references adde
On the Precision of a Length Measurement
We show that quantum mechanics and general relativity imply the existence of
a minimal length. To be more precise, we show that no operational device
subject to quantum mechanics, general relativity and causality could exclude
the discreteness of spacetime on lengths shorter than the Planck length. We
then consider the fundamental limit coming from quantum mechanics, general
relativity and causality on the precision of the measurement of a length.Comment: 5 pages, to appear in the proceedings of the 2006 International
School of Subnuclear Physics in Erice and in ''Young Scientists'' online-only
supplement of the European Physical Journal C-Direct (Springer
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