Pure NS-NS Flux Research Articles

Superstrings near the conformal boundary of AdS3

We study worldsheet sphere amplitudes, in the RNS formalism, in superstring theory on AdS3 × X with pure NS-NS flux using the near-boundary approximation. By computing a number of amplitudes at low-lying spectral flow, we deduce a candidate for a dual CFT for generic X. Specialising to X = S3 × \U0001d54b4 and with minimal NS-NS flux, i.e., to the tensionless limit, we explore the effect of the interaction term which we ignore in the near-boundary consideration. We show, under some assumptions, that amplitudes in the tensionless superstring theory on AdS3 × S3 × \U0001d54b4 do not receive perturbative contributions from such an interaction term.

Engineering perturbative string duals for symmetric product orbifold CFTs

Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide novel examples of string duals with and without supersymmetry. In this work we consider some marginal perturbation of a family of symmetric product orbifolds in two dimensions. From their correlation functions we engineer a bosonic string theory whose amplitudes are shown to reproduce the CFT correlation function order-by-order both in the coupling and in 1/N. Our derivation does not require to compute and compare correlation functions explicitly but rather relies on a sequence of identities that can be derived using path integral methods. The bosonic string theory we engineer is based on the field content of the Kac-Wakimoto representation of strings in AdS3 with k units of pure NSNS flux, but the interaction terms we obtain are different. They include current algebra preserving interaction terms with one unit of spectral flow.

Holographic Weyl anomaly in string theory

We compute the worldsheet sphere partition function of string theory on global AdS_33 with pure NS-NS flux. Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unambiguous. We show that it precisely reproduces the holographic Weyl anomaly and the ambiguous terms correspond to the possible counterterms of the boundary CFT.

Neumann-Rosochatius system for rotating strings in AdS3 × S3 × S3 × S1 with flux

We wish to construct an integrable Neumann-Rosochatius (NR) model of strings in AdS3 × S3 × S3 × S1 supported by pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations, which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only in S3 × S1. We further present a quantitative study on the rounding-off nature of the spike in the presence of non-zero angular momentum J in S1.

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

We continue our study of string correlators on Euclidean \text{AdS}_3AdS3 with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show that correlators exhibit a simple behaviour near their singularities. The spacetime correlators are meromorphic functions in the \mathrm{SL}(2,\mathbb{R})SL(2,ℝ)-spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual \text{CFT}_2CFT2. Moreover, we also compute the residues of the spacetime correlators for some of the poles exactly and find again a perfect match with the proposal for the dual \text{CFT}_2CFT2, thereby checking the duality for some non-trivial four-point functions exactly. Our computations simplify drastically in the tensionless limit of \mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4AdS3×S3×𝕋4 where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.

String correlators on AdS3: four-point functions

We propose a closed-form formula for genus 0 four-point functions in AdS3 string theory with pure NS-NS flux including arbitrary amounts of spectral flow. Our formula passes many non-trivial consistency checks and has intriguing connections to Hurwitz theory. This paper is the second in a series with several instalments.

String theory on AdS3 and the symmetric orbifold of Liouville theory

For string theory on AdS3 with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows us to show that the long string sector of superstring theory on AdS3×S3×T4 for generic NS-NS flux is described by the symmetric orbifold of (N=4Liouville theory)×T4. For the case of minimal flux (k=1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T4, thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS×3X.

Strings on AdS3 \xd7 S3 \xd7 S3 \xd7 S1

String theory on AdS3 × S3 × S3 × S1 with pure NS-NS flux and minimal flux through one of the two S3’s is studied from a world-sheet perspective. It is shown that the spacetime spectrum, as well as the algebra of spectrum generating operators, matches precisely that of the symmetric orbifold of S3 × S1 in the large N limit. This gives strong support for the proposal that these two descriptions are exactly dual to one another.

Minimal surfaces with mixed three-form flux

We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model. We find that the NS-NS flux term either brings the surface near to the boundary or separates the circumferences. In the limit of pure NS-NS flux the solution adheres to the boundary in the former case and the outer radius diverges in the latter. We further construct the underlying elliptic spectral curve, which allows us to analyze the deformation of other related minimal surfaces. We show that in the regime of pure NS-NS flux the elliptic curve degenerates.

Long strings and chiral primaries in the hybrid formalism

We revisit two related phenomena in AdS3 string theory backgrounds. At pure NS-NS flux, the spectrum contains a continuum of long strings which can escape to the boundary of AdS3 at a finite cost of energy. Related to this are certain gaps in the BPS spectrum one computes from the RNS worldsheet description. One expects that both these effects disappear when perturbing slightly away from the pure NS-NS flux background. We employ the hybrid formalism for mixed flux backgrounds to demonstrate directly from the worldsheet that this is indeed the case.

The plane-wave limit of AdS3\xd7S3\xd7S3\xd7S1

The plane-wave limit of AdS3 ×S3 ×S3 ×S1 is analysed for generic null-geodesics that are not necessarily BPS. For the case of pure NS-NS flux it is shown how the resulting spectrum can be reproduced as a suitable limit of the world-sheet description in terms of WZW models. Since supersymmetry is broken, most of the degeneracies are lifted, and thus the identification of states is quite unambiguous.

On multi-spin classical strings with NS-NS flux

We study multi spin semiclassical strings in AdS3 × S3 × T4 background supported by a mixture of Neveu-Schwarz-Neveu-Schwarz (NS-NS) and Ramond-Ramond (R-R) fluxes. This ‘mixed flux’ background has been recently proved to be classically integrable. We start with a particular rigidly spinning fundamental string in AdS3 ×S1 coupled to the NS-NS flux and classify the possible profiles. We also find out how the scaling relation among the energy and angular momenta of such a string changes due to presence of these fluxes. We emphasize on pure NS-NS flux case and discuss the fate of such solutions in that limit.

Tensionless string spectra on AdS3

The spectrum of superstrings on AdS3 × S3 × mathbb{M} 4 with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value (k = 1). Both for mathbb{M} 4 = S3 × S1 and mathbb{M} 4 = mathbb{T} 4 we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of AdS3 × S3 × mathbb{T} 4 this relies on making sense of the world-sheet theory at k = 1, for which we make a concrete proposal. We also comment on the implications of this striking result.

Pulsating strings with mixed three-form flux

Circular strings pulsating in AdS3 × S3 × T4 with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in AdS3 with pure NS-NS three-form flux, where the action reduces to the SL(2, ℝ) WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow by Maldacena and Ooguri. We use our elliptic solutions in AdS3 to extend the dispersion relation beyond the limit of pure NS-NS flux.

Supersymmetric AdS3 supergravity backgrounds and holography

We analyse the conditions for AdS3 × ℳ7 backgrounds with pure NS-NS flux to be supersymmetric. We classify all mathcal{N}=left(2, 2right) solutions where ℳ7 satisfies the stronger condition of being a U(1)-fibration over a Kähler manifold. We compute the BPS spectrum of all the backgrounds in this classification. We assign a natural dual CFT to the backgrounds and confirm that the BPS spectra agree, thus providing evidence in favour of the proposal.

Higher spins on AdS3 from the worldsheet

It was recently shown that the CFT dual of string theory on AdS3 × S3 × T4, the symmetric orbifold of T4, contains a closed higher spin subsector. Via holography, this makes precise the sense in which tensionless string theory on this background contains a Vasiliev higher spin theory. In this paper we study this phenomenon directly from the worldsheet. Using the WZW description of the background with pure NS-NS flux, we identify the states that make up the leading Regge trajectory and show that they fit into the even spin mathcal{N}=4 Vasiliev higher spin theory. We also show that these higher spin states do not become massless, except for the somewhat singular case of level k = 1 where the theory contains a stringy tower of massless higher spin fields coming from the long string sector.

Multi-spike strings in AdS3 with mixed three-form fluxes

The string sigma model in AdS3 ×S 3 supported by mixed three-form fluxes has recently been proved to be integrable which led to a plethora of work in this background including proposals for S matrix and study of semiclassical string profiles. Motivated by this, in this paper, we present a study of ‘spiky’ strings in this background. We analyze the string profiles in detail and also find the dispersion relation between the charges in the ‘long’ string limit after solving the equations of motion perturbatively upto the leading order in the Neveu-Schwarz flux b. We find that the dispersion for 2 spikes gets corrected by the term $$ -\frac{b^2}{2} $$ log S. We also discuss the fate of the solution in the limit of pure NS-NS flux.

Elliptic solutions in the Neumann–Rosochatius system with mixed flux

Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS three-form fluxes are described by a deformation of the one-dimensional Neumann-Rosochatius integrable system. In this article we find general solutions to this system that can be expressed in terms of elliptic functions. We consider closed strings rotating either in S^3 with two different angular momenta or in AdS_3 with one spin. In order to find the solutions we will need to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system to include the contribution from the flux. In the limit of pure NS-NS flux, where the problem can be described by a supersymmetric WZW model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.

On string theory on [formula omitted] with mixed 3-form flux: Tree-level S-matrix

We consider superstring theory on AdS3×S3×T4 supported by a combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q). This theory interpolates between the pure RR flux model (q=0) whose spectrum is expected to be described by a (thermodynamic) Bethe ansatz and the pure NSNS flux model (q=1) which is described by the supersymmetric extension of the SL(2,R)×SU(2) WZW model. As a first step towards the solution of this integrable theory for generic value of q we compute the corresponding tree-level S-matrix for massive BMN-type excitations. We find that this S-matrix has a surprisingly simple dependence on q: the diagonal amplitudes have exactly the same structure as in the q=0 case but with the BMN dispersion relation e2=p2+1 replaced by the one with shifted momentum and mass, e2=(p±q)2+1−q2. The off-diagonal amplitudes are then determined from the classical Yang–Baxter equation. We also construct the Pohlmeyer-reduced model corresponding to this superstring theory and find that it depends on q only through the rescaled mass parameter, μ→1−q2μ, implying that its relativistic S-matrix is q-independent.

The massless string spectrum on AdS3 × S 3 from the supergroup

String theory on AdS_3 x S^3 is studied in the hybrid formulation. We give a detailed description of the PSL(2|2) supergroup WZW model that underlies the background with pure NS-NS flux, and determine the BRST-cohomology corresponding to the massless string states. The resulting spectrum is shown to match exactly with the expected supergravity answer, including the sectors with small KK momentum on the sphere.