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

On spectrally flowed local vertex operators in AdS3_3

We provide a novel local definition for spectrally flowed vertex operators in the SL(2,$\mathbb{R}$)-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega > 1$. 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 $y$ 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 $y$-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of the SL(2,$\mathbb{R}$) series identifications in this context, and prove the validity of the conjecture put forward in [arXiv:2105.12130] for $y$-space structure constants of three-point functions with arbitrary spectral flow charges.Comment: 25 page

A proof for string three-point functions in AdS3_3

Correlation functions of the $\text{SL}(2,\mathbb{R})$-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 $\text{SL}(2,\mathbb{R})$ 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$_3$/CFT$_2$ 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 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

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

Spectral flow and string correlators in AdS3×S3×T4_3\times S^3 \times T^4

We consider three-point correlation functions for superstrings propagating in AdS$_3\times S^3 \times T^4$. In the RNS formalism, these generically involve correlators with current insertions. When vertex operators with non-trivial spectral flow charges are present, their complicated OPEs with the currents imply that standard methods can not be used to compute such correlators. Here we develop novel techniques for computing all $m$-basis correlators of the supersymmetric model. We then show how, in some cases, these results can be translated to the $x$-basis. We obtain a new family of holographic three-point functions involving spacetime chiral primaries living in spectrally flowed sectors of the worldsheet CFT. These match precisely the predictions from the holographic dual at the symmetric product orbifold point. Finally, we also consider long strings and compute the probability amplitude associated with the process describing the emission/absorption of fundamental string quanta.Comment: 35 page