15 research outputs found
Analytic Expressions for Singular Vectors of the Superconformal Algebra
Using explicit expressions for a class of singular vectors of the
(untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and
Kent, we show that the analytically extended Verma modules contain two linearly
independent neutral singular vectors at the same grade. We construct this two
dimensional space and we identify the singular vectors of the original Verma
modules. We show that in some Verma modules these expressions lead to two
linearly independent singular vectors which are at the same grade and have the
same charge.Comment: 35 pages, LATE
Current-Current Deformations of Conformal Field Theories, and WZW Models
Moduli spaces of conformal field theories corresponding to current-current
deformations are discussed. For WZW models, CFT and sigma model considerations
are compared. It is shown that current-current deformed WZW models have
WZW-like sigma model descriptions with non-bi-invariant metrics, additional
B-fields and a non-trivial dilaton.Comment: 30 pages, latex, v2: remarks and references adde
On the complete classification of the unitary N=2 minimal superconformal field theories
Aiming at a complete classification of unitary N=2 minimal models (where the
assumption of space-time supersymmetry has been dropped), it is shown that each
modular invariant candidate of a partition function for such a theory is indeed
the partition function of a minimal model. A family of models constructed via
orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models demonstrates that there exists a unitary N=2 minimal model
for every one of the allowed partition functions in the list obtained from
Gannon's work.
Kreuzer and Schellekens' conjecture that all simple current invariants can be
obtained as orbifolds of the diagonal model, even when the extra assumption of
higher-genus modular invariance is dropped, is confirmed in the case of the
unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references
added, typos corrected, footnote added on p31; renumbering of sections; main
theorem reformulated for clarity, but contents unchanged. Minor revisions in
v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2
rewritten for greater generality, section 3.3 review removed. To appear in
Comm. Math. Phy
Unitarity of rational N=2 superconformal theories
We demonstrate that all rational models of the N=2 super Virasoro algebra are
unitary. Our arguments are based on three different methods: we determine Zhu's
algebra (for which we give a physically motivated derivation) explicitly for
certain theories, we analyse the modular properties of some of the vacuum
characters, and we use the coset realisation of the algebra in terms of su_2
and two free fermions.
Some of our arguments generalise to the Kazama-Suzuki models indicating that
all rational N=2 supersymmetric models might be unitary.Comment: LaTeX (+amssym.def), 28 pages; minor changes in content, some
references added, final versio
Type 0 Strings in a 2-d Black Hole
We study some aspects of type 0 strings propagating in the two dimensional
black hole geometry, corresponding to the exact SL(2)/U(1) SCFT background.Comment: 33 pages, harvmac. v2: minor clarification adde
On the Quantum Invariant for the Spherical Seifert Manifold
We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert
manifold where is a finite subgroup of SU(2). We show
that the WRT invariants can be written in terms of the Eichler integral of the
modular forms with half-integral weight, and we give an exact asymptotic
expansion of the invariants by use of the nearly modular property of the
Eichler integral. We further discuss that those modular forms have a direct
connection with the polyhedral group by showing that the invariant polynomials
of modular forms satisfy the polyhedral equations associated to .Comment: 36 page
Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk
An analysis of a spherically symmetric braneworld configuration is performed
when the intrinsic curvature scalar is included in the bulk action; the
vanishing of the electric part of the Weyl tensor is used as the boundary
condition for the embedding of the brane in the bulk. All the solutions outside
a static localized matter distribution are found; some of them are of the
Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior
solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior,
while the other does not. A non-universal gravitational constant arises,
depending on the density of the considered object; however, the conventional
limits of the Newton's constant are recovered. An upper bound of the order of
TeV for the energy string scale is extracted from the known solar system
measurements (experiments). On the contrary, in usual brane dynamics, this
string scale is calculated to be larger than TeV.Comment: 23 pages, 1 figure, one minor chang
Strings in homogeneous gravitational waves and null holography
Homogeneous gravitational wave backgrounds arise as infinite momentum limits of many geometries with a well-understood holographic description. General global aspects of these geometries are discussed. Using exact CFT techniques, strings in pp-wave backgrounds supported by a Neveu-Schwarz flux are quantized. As in Euclidean , spectral flow and associated long strings are shown to be crucial in obtaining a complete spectrum. Holography is investigated in such backgrounds, using conformally flat coordinates analogous to those of the Poincar\'e patch in AdS. It is argued that the holographic direction is the light-cone null coordinate . It is proposed that the holographic degrees of freedom live on a codimension-one screen at fixed (possibly dimensionally reduced due to the confining harmonic potentiel in transverse space). A complementary screen at fixed is argued to be necessary in order to encode the vacuum structure