36,128 research outputs found
N=1 extension of minimal model holography
The CFT dual of the higher spin theory with minimal N = 1 spectrum is
determined. Unlike previous examples of minimal model holography, there is no
free parameter beyond the central charge, and the CFT can be described in terms
of a non-diagonal modular invariant of the bosonic theory at the special value
of the 't Hooft parameter lambda=1/2. As evidence in favour of the duality we
show that the symmetry algebras as well as the partition functions agree
between the two descriptions.Comment: 28 page
Conformal covariance of massless free nets
In the present paper we review in a fibre bundle context the covariant and
massless canonical representations of the Poincare' group as well as certain
unitary representations of the conformal group (in 4 dimensions). We give a
simplified proof of the well-known fact that massless canonical representations
with discrete helicity extend to unitary and irreducible representations of the
conformal group mentioned before. Further we give a simple new proof that
massless free nets for any helicity value are covariant under the conformal
group. Free nets are the result of a direct (i.e. independent of any explicit
use of quantum fields) and natural way of constructing nets of abstract
C*-algebras indexed by open and bounded regions in Minkowski space that satisfy
standard axioms of local quantum physics. We also give a group theoretical
interpretation of the embedding {\got I} that completely characterizes the
free net: it reduces the (algebraically) reducible covariant representation in
terms of the unitary canonical ones. Finally, as a consequence of the conformal
covariance we also mention for these models some of the expected algebraic
properties that are a direct consequence of the conformal covariance (essential
duality, PCT--symmetry etc.).Comment: 31 pages, Latex2
Holography and SL(2,\bR) symmetry in 2D Rindler spacetime
It is shown that it is possible to define quantum field theory of a massless
scalar free field on the Killing horizon of a 2D-Rindler spacetime. Free
quantum field theory on the horizon enjoys diffeomorphism invariance and turns
out to be unitarily and algebraically equivalent to the analogous theory of a
scalar field propagating inside Rindler spacetime, nomatter the value of the
mass of the field in the bulk. More precisely, there exists a unitary
transformation that realizes the bulk-boundary correspondence under an
appropriate choice for Fock representation spaces. Secondly, the found
correspondence is a subcase of an analogous algebraic correspondence described
by injective *-homomorphisms of the abstract algebras of observables generated
by abstract quantum free-field operators. These field operators are smeared
with suitable test functions in the bulk and exact 1-forms on the horizon. In
this sense the correspondence is independent from the chosen vacua. It is
proven that, under that correspondence the ``hidden'' SL(2,\bR) quantum
symmetry found in a previous work gets a clear geometric meaning, it being
associated with a group of diffeomorphisms of the horizon itself.Comment: Title changed, further minor changes, references added, accepted for
publication in J. Math. Phy
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