More AdS_3 correlators

We compute three-point functions for the $SL(2,\mathbb R)$-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

Spectral flow and conformal blocks in AdS3

In this article we investigate the structure of the four-point functions of the AdS3-WZNW model. We consider the integral expression for the unflowed four-point correlator involving at least one state in the discrete part of the spectrum derived by analytic continuation from the H+3 -WZNW model and we show that the conformal blocks can be obtained from those with an extremal-weight state by means of an intertwining operator. We adapt the procedure for dealing with correlators with a single unit of spectral flow charge and we get a factorized integral expression for the corresponding four-point function. We finally transform the formulas back to the space-time picture.Fil: Cagnacci, Yago Javier. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Iguri, Sergio Manuel. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

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.

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 $A$, the space \hilb_A(A^*) of the Hilbert spaces that are continuously embedded in $A^*$ and are $^*$-invariant under the dual left regular action of $A$ 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

Coulomb integrals for the SL(2,R) WZNW model

We review the Coulomb gas computation of three-point functions in the SL(2,R) WZNW model and obtain explicit expressions for generic states. These amplitudes have been computed in the past by this and other methods but the analytic continuation in the number of screening charges required by the Coulomb gas formalism had only been performed in particular cases. After showing that ghost contributions to the correlators can be generally expressed in terms of Schur polynomials we solve Aomoto integrals in the complex plane, a new set of multiple integrals of Dotsenko-Fateev type. We then make use of monodromy invariance to analytically continue the number of screening operators and prove that this procedure gives results in complete agreement with the amplitudes obtained from the bootstrap approach. We also compute a four-point function involving a spectral flow operator and we verify that it leads to the one unit spectral flow three-point function according to a prescription previously proposed in the literature. In addition, we present an alternative method to obtain spectral flow non-conserving n-point functions through well defined operators and we prove that it reproduces the exact correlators for n=3. Independence of the result on the insertion points of these operators suggests that it is possible to violate winding number conservation modifying the background charge.Comment: Improved presentation. New section on spectral flow violating correlators and computation of a four-point functio

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 Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); Argentina;Fil: Penas, Victor Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina

Minimal irreversible quantum mechanics. The decay of unstable states

Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution that is used to study the time evolution of the reduced density operator. It is derived in a closed form, in the one-particle sector of the model. The irreversible behavior of the Brownian particle is described by a reduced density matrix.Comment: 39 pages, 2 figure