721 research outputs found
Intersecting Jones projections
Let 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,\cdot\Omega). Moreover, let {N_i :i\in I} be a
family of von Neumann subalgebras of M with faithful normal conditional
expectations E_i of M onto N_i satisfying \omega=\omega\circ E_i for all i\in I
and let N=\bigcap_{i\in I} N_i. We show that the projections e_i, e of H onto
the closed subspaces \bar{N_i\Omega} and \bar{N\Omega} respectively satisfy
e=\bigwedge_{i\in I}e_i.This proves a conjecture of V.F.R. Jones and F. Xu in
\cite{JonesXu04}
Energy bounds for vertex operator algebra extensions
Let 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
La resistenza culturale nel Libano contemporaneo. Le sfide di artiste locali e profughe = Cultural resistance in contemporary Lebanon: The challenges of local and refugee artists
Sulla base di interviste condotte nel 2018, questo articolo analizza le somiglianze e le differenze che intercorrono tra le sfide che i âfautori della culturaâ â artiste in primis â cittadine libanesi e rifugiate palestinesi e siriane devono affrontare nel contesto libanese. Dopo unâillustrazione dello scenario storico-politico libanese e di come in esso la âresistenza culturaleâ emerge in modo poliedrico, gli autori individuano aree dâincontro e di potenziale solidarietĂ tra gruppi. Lâarticolo discute la cosiddetta âumanitarizzazioneâ dei finanziamenti, attraverso la quale vengono sostenuti e potenziati soprattutto i progetti artistici che possono fungere da strumento di neutralitĂ politica e di âmedicalizzazioneâ dei traumi post-guerra. Tale fenomeno genera in parte una depoliticizzazione ed esteticizzazione dellâarte, âdemobilitandoâ quindi la verve politica dietro al lavoro culturale e, allo stesso tempo, lega la sopravvivenza materiale di tali spazi culturali a cicliche crisi umanitarie
Classification of subsystems, local symmetry generators and intrinsic definition of local observables
We give a general overview of results about subsystems of local nets of von Neumann algebras in close connection with the problem of characterizing the abstract algebra of observables through the existence of Wightman currents
Thermal States in Conformal QFT. II
We continue the analysis of the set of locally normal KMS states w.r.t. the
translation group for a local conformal net A of von Neumann algebras on the
real line. In the first part we have proved the uniqueness of KMS state on
every completely rational net. In this second part, we exhibit several
(non-rational) conformal nets which admit continuously many primary KMS states.
We give a complete classification of the KMS states on the U(1)-current net and
on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro
net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many
primary KMS states. To this end, we provide a variation of the
Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework:
if there is an inclusion of split nets A in B and A is the fixed point of B
w.r.t. a compact gauge group, then any locally normal, primary KMS state on A
extends to a locally normal, primary state on B, KMS w.r.t. a perturbed
translation. Concerning the non-local case, we show that the free Fermi model
admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his
90th birthday. The final version is available under Open Access. This paper
contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a
proof of the same theorem in the book by Bratteli-Robinson). v3: a reference
correcte
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
We study the representation theory of a conformal net A on the circle from a
K-theoretical point of view using its universal C*-algebra C*(A). We prove that
if A satisfies the split property then, for every representation \pi of A with
finite statistical dimension, \pi(C*(A)) is weakly closed and hence a finite
direct sum of type I_\infty factors. We define the more manageable locally
normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest
ideal vanishing in all locally normal representations and we investigate its
structure. In particular, if A is completely rational with n sectors, then
C*_ln(A) is a direct sum of n type I_\infty factors. Its ideal K_A of compact
operators has nontrivial K-theory, and we prove that the DHR endomorphisms of
C*(A) with finite statistical dimension act on K_A, giving rise to an action of
the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this
action corresponds to the regular representation of the associated fusion
algebra.Comment: v2: we added some comments in the introduction and new references.
v3: new authors' addresses, minor corrections. To appear in Commun. Math.
Phys. v4: minor corrections, updated reference
Super-KMS functionals for graded-local conformal nets
Motivated by a few preceding papers and a question of R. Longo, we introduce
super-KMS functionals for graded translation-covariant nets over R with
superderivations, roughly speaking as a certain supersymmetric modification of
classical KMS states on translation-covariant nets over R, fundamental objects
in chiral algebraic quantum field theory. Although we are able to make a few
statements concerning their general structure, most properties will be studied
in the setting of specific graded-local (super-) conformal models. In
particular, we provide a constructive existence and partial uniqueness proof of
super-KMS functionals for the supersymmetric free field, for certain subnets,
and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a
separate result, we classify bounded super-KMS functionals for graded-local
conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare
Unitary representations of the W3-algebra with c â„ 2
We prove unitarity of the vacuum representation of the W_3-algebra for all values of the central charge c ℠2.We do it by modifying the free field realization of Fateev and Zamolodchikov resulting in a representation which, by a nontrivial argument, can be shown to be unitary on a certain invariant subspace, although it is not unitary on the full space of the two currents needed for the construction. These vacuum representations give rise to simple unitary vertex operator algebras. We also construct explicitly unitary representations for many positive lowest weight values. Taking into account the known form of the Kac determinants, we then completely clarify the question of unitarity of the irreducible lowest weight representations of the W_3-algebra in the 2 †c †98 region
Representations of conformal nets, universal C*-algebras and K-theory
We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal
C*-algebra C*(A). We prove that if A satisfies the split property then, for every representation pi of A with finite statistical dimension, pi(C*(A)) is weakly closed and hence a finite direct sum of type I_infty factors. We define the more manageable locally normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with n sectors, then
C*_ln(A) is a direct sum of n type I_infty factors. Its ideal K_A of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of C*(A) with finite statistical dimension act on K_A, giving rise to an action of the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra
Spectral triples and the super-Virasoro algebra
We construct infinite dimensional spectral triples associated with
representations of the super-Virasoro algebra. In particular the irreducible,
unitary positive energy representation of the Ramond algebra with central
charge c and minimal lowest weight h=c/24 is graded and gives rise to a net of
even theta-summable spectral triples with non-zero Fredholm index. The
irreducible unitary positive energy representations of the Neveu-Schwarz
algebra give rise to nets of even theta-summable generalised spectral triples
where there is no Dirac operator but only a superderivation.Comment: 27 pages; v2: a comment concerning the difficulty in defining cyclic
cocycles in the NS case have been adde
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