1,721,027 research outputs found
Quantum Noether's theorem and conformal field theory: a study of some models
Full text linkWe study the problem of recovering Wightman conserved currents from
the canonical local implementations of symmetries which can be
constructed in the algebraic framework of quantum field theory, in the
limit in which the region of localization shrinks to a point. We show that, in
a class of models of conformal quantum field theory in space-time
dimension 1+1, which includes the free massless scalar field and the
SU(N) chiral current algebras, the energy-momentum tensor can be
recovered. Moreover we show that the scaling limit of the canonical local
implementation of SO(2) in the free complex scalar field is zero, a
manifestation of the fact that, in this last case, the associated Wightman
current does not exist
On the representation theory of Virasoro nets
Full text linkWe discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the c=1 Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge c is in a certain subset of (1,infty), including [2,infty ), and h geq (c-1)/24, the irreducible representation with lowest weight h of the corresponding Virasoro net has infinite statistical dimension. As a consequence we show that if the central charge c is in the above set and satisfies cleq 25 then the corresponding Virasoro net has no proper local extensions of compact type
Classification of subsystems for the Haag-Kastler nets generated by c=1 chiral current algebras
Full text linkLet F be the Haag-Kastler net generated by the su(2) chiral current algebra at level 1. We classify the
SL(2, R)-covariant subsystems B subset F by showing that they are all fixed points nets F^H for some subgroup H of the gauge automorphisms group SO(3) of F. Then using the fact that the net F_1 generated by the u(1)
chiral current can be regarded as a subsystem of F we classify the subsystems of F_1. In this case there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge
invariant subsystem F_1^{Z_2}
Absence of subsystems for the Haag-Kastler net generated by the energy-momentum tensor in two-dimensional conformal field theory
Full text linkWe show that if A is the Haag-Kastler net generated by the energy-momentum tensor in a chiral quantum field theory, then every subsystem B subset A which is covariant under the action of SL(2,R) given on A must coincide with A. The result is valid for all the allowed values of the central charge and is obtained using scaling limit techniques
Intersecting Jones projections
Full text linkLet M be a von Neumann algebra on a Hilbert space H with a cyclic and separating unit vector Omega and let omega be the faithful normal state on M given by omega(cdot)=(Omega,cdotOmega). Moreover, let {N_i :iin I} be a family of von Neumann subalgebras of M with faithful normal conditional expectations E_i of onto N_i satisfying
omega=omegacirc E_i for all iin I and let N=igcap_{iin I} N_i. We show that the projections e_i, e of H onto the closed subspaces overline{N_iOmega} and overline{NOmega} respectively satisfy e=igwedge_{iin I}e_i. This proves a conjecture of V.F.R. Jones and F. Xu
The Virasoro algebra and sectors with infinite statistical dimension
Full text linkWe show that the sectors with lowest weight h geq 0, h
eq j^2, j in (1/2)Z of the local net of von Neumann algebras on the circle generated by the Virasoro algebra with central charge c=1 have infinite statistical dimension
Energy bounds for vertex operator algebra extensions
Full text linkLet V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is that U is a compact orbifold for some compact group G of unitary automorphisms of V. The second condition is that V is exponentially energy-bounded and it is a finite direct sum of simple U-modules. As consequence of the second condition, we prove that if U is a regular energy-bounded unitary subalgebra of a simple unitary vertex operator V, then V is energy-bounded. In particular, every simple unitary extension (with the same conformal vector) of a simple unitary affine vertex operator algebra associated with a semisimple Lie algebra is energy-bounded
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