15,986 research outputs found
How to add a boundary condition
Given a conformal QFT local net of von Neumann algebras B_2 on the
two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A
is a completely rational net on the left/right light-ray, we show how to
consistently add a boundary to B_2: we provide a procedure to construct a
Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated
with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT
nets arise in this way. There are only finitely many locally isomorphic
Boundary CFT nets and we get them all together. In essence, we show how to
directly redefine the C* representation of the restriction of B_2 to the
half-plane by means of subfactors and local conformal nets of von Neumann
algebras on S^1.Comment: 20 page
The classification of non-local chiral CFT with c<1
All non-local but relatively local irreducible extensions of Virasoro chiral
CFTs with c<1 are classified. The classification, which is a prerequisite for
the classification of local c<1 boundary CFTs on a two-dimensional half-space,
turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished
vertices.Comment: 13 pages. v3: additional material (concerning the Hilbert spaces)
adde
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
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
A Remark on Quantum Group Actions and Nuclearity
Let H be a compact quantum group with faithful Haar measure and bounded
counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if
its fixed-point subalgebra is nuclear. As a consequence H is a nuclear
C*-algebra.Comment: 12 pages, LateX 2
On intermediate subfactors of Goodman-de la Harpe-Jones subfactors
In this paper we present a conjecture on intermediate subfactors which is a
generalization of Wall's conjecture from the theory of finite groups. Motivated
by this conjecture, we determine all intermediate subfactors of
Goodman-Harpe-Jones subfactors, and as a result we verify that
Goodman-Harpe-Jones subfactors verify our conjecture. Our result also gives a
negative answer to a question motivated by a conjecture of
Aschbacher-Guralnick.Comment: To appear in Comm. Math. Phy
Some computations in the cyclic permutations of completely rational nets
In this paper we calculate certain chiral quantities from the cyclic
permutation orbifold of a general completely rational net. We determine the
fusion of a fundamental soliton, and by suitably modified arguments of A. Coste
, T. Gannon and especially P. Bantay to our setting we are able to prove a
number of arithmetic properties including congruence subgroup properties for
matrices of a completely rational net defined by K.-H. Rehren .Comment: 30 Pages Late
The Conformal Spin and Statistics Theorem
We prove the equality between the statistics phase and the conformal
univalence for a superselection sector with finite index in Conformal Quantum
Field Theory on . A relevant point is the description of the PCT symmetry
and the construction of the global conjugate charge.Comment: plain tex, 22 page
Charged sectors, spin and statistics in quantum field theory on curved spacetimes
The first part of this paper extends the Doplicher-Haag-Roberts theory of
superselection sectors to quantum field theory on arbitrary globally hyperbolic
spacetimes. The statistics of a superselection sector may be defined as in flat
spacetime and each charge has a conjugate charge when the spacetime possesses
non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes
with appropriate symmetries. Two situations are considered: First, if the
spacetime has a bifurcate Killing horizon, as is the case in the presence of
black holes, then restricting the observables to the Killing horizon together
with "modular covariance" for the Killing flow yields a conformally covariant
quantum field theory on the circle and a conformal spin-statistics theorem for
charged sectors localizable on the Killing horizon. Secondly, if the spacetime
has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes,
"geometric modular action" of the rotational symmetry leads to a
spin-statistics theorem for charged covariant sectors where the spin is defined
via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page
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