Aspects of the free field description of string theory on AdS 3

2004

The main purpose of the report is to provide some argumentation that three seemingly distinct approaches of 1. Giveon, Kutasov and Seiberg (hep-th/9806194); 2. Hemming, Keski-Vakkuri (hep-th/0110252); Maldacena, Ooguri (hep-th/0001053) and 3. I. Bars (hep-th/9503205) can be investigated by applying the mathematical methods of integral geometry on the Lobachevsky plane, developed previously by Gel'fand, Graev and Vilenkin. All these methods can be used for finding the transformations, leaving the Kac-Moody and Virasoro algebras invariant. The near-distance limit of the Conformal Field Theory of the SL(2, R) WZW model of strings on an ADS3 background can also be interpreted in terms of the Lobachevsky Geometry : the non - euclidean distance is conserved and the Lobachevsky formulae for the angle of parallelism is recovered. Some preliminary technique from integral geometry for inverting the modified integral representation for the Kac- Moody algebra has been demonstrated.

International Journal of Modern Physics D, 2020

We review old and recent results on a special limit of string theory on [Formula: see text] with pure NS–NS fluxes: the limit in which the string length [Formula: see text] equals the [Formula: see text] radius [Formula: see text]. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the noncompactness of the boundary CFT target space, and on how these features change when the point [Formula: see text] is approached. Also, we briefly review the recent proposals for exact realizations of AdS/CFT correspondence at this special point.

2003

We study bosonic string theory in the light-cone gauge on AdS 3 spacetime with zero radius of curvature (in string units) R/ √ α ′ = 0. We find that the worldsheet theory admits an infinite number of conserved quantities which are naturally interpreted as spacetime charges and which form a representation of (two commuting copies of) a Virasoro algebra. Near the boundary of AdS 3 these charges are found to be isomorphic to the infinite set of asymptotic Killing vectors of AdS 3 found originally by Brown and Henneaux. In addition to the spacetime Virasoro algebra, there is a worldsheet Virasoro algebra that generates diffeomorphisms of the spatial coordinate of the string worldsheet. We find that if the worldsheet Virasoro algebra has a central extension then the spacetime Virasoro algebra acquires a central extension via a mechanism similar to that encountered in the context of the SL(2, R) WZW model. Our observations are consistent with a recently proposed duality between bosonic strings on zero radius AdS d+1 and free field theory in d dimensions.

2002

The SL(2, R) WZW model of strings on an ADS3 background is investigated in the spirit of J.Maldacena's and H.Ooguri's approach (hep-th/0001053 and hep-th/0005183). Choosing a standard, but most general three-variable parametrization of the SL(2, R) group element g, the system of equations for the Operator Product Expansion (OPE) relations is analysed. In the investigated SL(2, R) case, this system is consistent if each three points on the complex plane lie on a certain hypersurface in CP3. A system of three nonlinear first-order differential equations has been obtained for the parametrization functions. It was demonstrated also how the mathematical apparatus of generalized functions and integral geometry can be implemented in order to modify the integral operators, entering the Kac-Moody and Virasoro algebras.

HAL (Le Centre pour la Communication Scientifique Directe), 2010

We first clarify the relation between boundary perturbations of AdS 3 in general relativity, and exactly marginal worldsheet vertex operators in AdS 3 string theory with Neveu-Schwarz Neveu-Schwarz flux. The latter correspond to solutions of the higher derivative low-energy tree level effective action to all orders in the string length over the curvature radius. We then calculate the exact expression of the boundary energy momentum tensor including all these higher derivative corrections in a purely bosonic string theory. The bottom-line is a canonical shift in the normalization of the boundary energy-momentum tensor corresponding to a shift in the curvature radius over the string length squared by the dual Coxeter number of the SL(2, R) subalgebra of the space-time Virasoro algebra. That allows us to derive the value of the Brown-Henneaux central charge including all tree level higher derivative corrections in bosonic string theory, in a scheme dictated by the worldsheet conformal field theory.

2021

Motivated by recent works in which the FZZ duality plays an important role, we revisit the computation of correlation functions in the sine-Liouville field theory. We present a direct computation of the three-point function, the simplest to the best of our knowledge, and give expressions for the N -point functions in terms of integrated Liouville theory correlators. This leads us to discuss the relation to the H 3 WZW-Liouville correspondence, especially in the case in which spectral flow is taken into account. We explain how these results can be used to study scattering amplitudes of winding string states in AdS3. ar X iv :2 11 0. 04 19 7v 2 [ he pth ] 1 3 O ct 2 02 1

2013

We investigate N-point string scattering amplitudes in AdS3 space. Based on recent observations on the solutions of KZ and BPZ-type differential equations, we discuss how to describe the string theory in AdS3 as a marginal deformation of a (flat) linear dilaton background. This representation resembles the called “discrete light-cone Liouville ” realization as well as the FZZ dual description in terms of the sine-Liouville field theory. Consequently, the connection and differences between those and this realization are discussed. The free field representation presented here permits to understand the relation between correlators in both Liouville and WZNW theories in a very simple way. Within In this paper we study a representation of the N-point correlation functions describing string scattering amplitudes in Euclidean AdS3. The tree-level amplitudes of strings in this space were extensively studied in the literature and received renewed attention since the formulation of the AdS/CF...

Journal of High Energy Physics, 2008

We study the spectral flowed sectors of the H + 3 WZW model in the context of the holographic duality between type IIB string theory in AdS 3 × S 3 × T 4 with NSNS flux and the symmetric product orbifold of T 4 . We construct explicitly the physical vertex operators in the flowed sectors that belong to short representations of the superalgebra, thus completing the bulk-to-boundary dictionary for 1/2 BPS states. We perform a partial calculation of the string three-point functions of these operators. A complete calculation would require the threepoint couplings of non-extremal flowed operators in the H + 3 WZW model, which are at present unavailable. In the unflowed sector, perfect agreement has recently been found between the bulk and boundary three-point functions of 1/2 BPS operators. Assuming that this agreement persists in the flowed sectors, we determine certain unknown three-point couplings in the H + 3 WZW model in terms of three-point couplings of affine descendants in the SU(2) WZW model.

HAL (Le Centre pour la Communication Scientifique Directe), 2009

String theory on AdS 3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on P SU (1, 1|2), we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS 3 × S 3 with Ramond-Ramond fluxes. We also indicate how to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS 3 with Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems. Contents 1 Introduction 2 2 String Theory on AdS 3 × S 3 with Ramond-Ramond Fluxes 3 2.

arXiv (Cornell University), 2001

We propose a bosonic string/gauge theory correspondence by using IIB and 0B strings as a guide. Our construction is based on the low-energy bosonic string effective action in the presence of an extra form flux. The closed string tachyon can be stabilyzed if the AdS scale L does not exceed certain critical value, L<L_c. We argue that the extra form may be generated as a soliton from 3-string junctions, similarly to the known non-perturbative (Jackiw-Rebbi or 't Hooft-Hasenfratz) mechanism in gauge theories. The stable AdS_{13} x S^{13} solution is found, which apparently implies the existence of a 12-dimensional AdS-boundary conformal field theory with the SO(14) global symmetry in the large N 't Hooft limit. We also generalize the conjectured AdS/CFT duality to finite temperature, and calculate the `glueball' masses from the dilaton wave equation in the AdS black hole background, in various spacetime dimensions.