62 research outputs found
More AdS_3 correlators
We compute three-point functions for the -WZNW model. After
reviewing the case of the two-point correlator, we compute spectral flow
preserving and nonpreserving correlation functions in the space-time picture
involving three vertex operators carrying an arbitrary amount of spectral flow.
When only one or two insertions have nontrivial spectral flow numbers, the
method we employ allows us to find expressions without any constraint on the
spin values. Unlike these cases, the same procedure restrains the possible spin
configurations when three vertices belong to nonzero spectral flow sectors. We
perform several consistency checks on our results. In particular, we verify
that they are in complete agreement with previously computed correlators
involving states carrying a single unit of spectral flow.Comment: 22 pages. Minor changes. Some references adde
Coulomb integrals and conformal blocks in the AdS3-WZNW model
We study spectral flow preserving four-point correlation functions in the
AdS3-WZNW model using the Coulomb gas method on the sphere. We present a
multiple integral realization of the conformal blocks and explicitly compute
amplitudes involving operators with quantized values of the sum of their spins,
i.e., requiring an integer number of screening charges of the first kind. The
result is given as a sum over the independent configurations of screening
contours yielding a monodromy invariant expansion in powers of the worldsheet
moduli. We then examine the factorization limit and show that the leading terms
in the sum can be identified, in the semiclassical limit, with products of
spectral flow conserving three-point functions. These terms can be rewritten as
the m-basis version of the integral expression obtained by J. Teschner from a
postulate for the operator product expansion of normalizable states in the
H3+-WZNW model. Finally, we determine the equivalence between the
factorizations of a particular set of four-point functions into products of two
three-point functions either preserving or violating spectral flow number
conservation. Based on this analysis we argue that the expression for the
amplitude as an integral over the spin of the intermediate operators holds
beyond the semiclassical regime, thus corroborating that spectral flow
conserving correlators in the AdS3-WZNW model are related by analytic
continuation to correlation functions in the H3+-WZNW model.Comment: 28 pages; references modified, published versio
Some recursive formulas for Selberg-type integrals
A set of recursive relations satisfied by Selberg-type integrals involving
monomial symmetric polynomials are derived, generalizing previously known
results. These formulas provide a well-defined algorithm for computing
Selberg-Schur integrals whenever the Kostka numbers relating Schur functions
and the corresponding monomial polynomials are explicitly known. We illustrate
the usefulness of our results discussing some interesting examples.Comment: 11 pages. To appear in Jour. Phys.
On spectrally flowed local vertex operators in AdS
We provide a novel local definition for spectrally flowed vertex operators in
the SL(2,)-WZW model, generalising the proposal of Maldacena and
Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all . This allows us to establish the precise connection between the computation
of correlators using the so-called spectral flow operator, and the methods
introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local
Ward identities. We show that the auxiliary variable used in the latter
paper arises naturally from a point-splitting procedure in the space-time
coordinate. The recursion relations satisfied by spectrally flowed correlators,
which take the form of partial differential equations in -space, then
correspond to null-state conditions for generalised spectral flowed operators.
We highlight the role of the SL(2,) series identifications in this
context, and prove the validity of the conjecture put forward in
[arXiv:2105.12130] for -space structure constants of three-point functions
with arbitrary spectral flow charges.Comment: 25 page
Some remarks on the GNS representations of topological -algebras
After an appropriate restatement of the GNS construction for topological
-algebras we prove that there exists an isomorphism among the set
\cycl(A) of weakly continuous strongly cyclic -representations of a
barreled dual-separable -algebra with unit , the space \hilb_A(A^*) of
the Hilbert spaces that are continuously embedded in and are
-invariant under the dual left regular action of and the set of the
corresponding reproducing kernels. We show that these isomorphisms are cone
morphisms and we prove many interesting results that follow from this fact. We
discuss how these results can be used to describe cyclic representations on
more general inner product spaces.Comment: 34 pages. Minor changes. To appear in J. Math. Phys. 49 (4) Apr-0
A proof for string three-point functions in AdS
Correlation functions of the -WZW model involving
spectrally flowed vertex operators are notoriously difficult to compute. An
explicit integral expression for the corresponding three-point functions was
recently conjectured in [arXiv:2105.12130v2]. In this paper, we provide a proof
for this conjecture. For this, we extend the methods of [arXiv:2208.00978]
based on the so-called series identifications, which
relate vertex operators belonging to different spectral flow sectors. We also
highlight the role of holomorphic covering maps in this context. Our results
constitute an important milestone for proving this instance of the
AdS/CFT holographic duality at finite 't Hooft coupling.Comment: 22 page
Duality phases and halved maximal D=4 supergravity
The duality angles deformation developed by de Roo and Wagemans within the context of N=4 gauged supergravity is used in order to study certain classes of gaugings of N=8 supergravity, namely, those that are consistent when halving the maximal D=4 theory. After reviewing the truncation process from N=8 to N=4 supergravity in terms of the embedding tensor formalism, the de Roo-Wagemans phases method is implemented for solving the resulting constraints on the gauging parameters by means of the Schon-Weidner ansatz. In contrast with the twenty semisimple N=4 gaugings admitting more than a single SL(2) angle deforming their decompositions reported in the literature, it is proven that only three of them can be embedded back into the N=8 theory. The scalar potential derived for only two of these gauge groups exhibits an extremum in the origin of the scalar manifold. These extrema are not stable under fluctuations of all the scalar fields.Fil: Iguri, Sergio Manuel. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de AstronomÃa y FÃsica del Espacio(i); Argentina;Fil: Penas, Victor Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FÃsica; Argentina
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