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We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS 3 ×$$\\mathcal{N}$$with NS-NS flux and a single-trace$$T\\overline{T }$$deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the$$T\\overline{T }$$deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with$$h+2\\frac{\\widetilde{\\lambda }}{w}p\\overline{p }$$, where h is the spacetime conformal weight,$$\\widetilde{\\lambda }$$is a deformation parameter, p and$$\\overline{p }$$are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace$$T\\overline{T }$$deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured$${\\text{TsT}}/T\\overline{T }$$correspondence.

A bstract Superstring theory on AdS 3 × S 3 × T 4 with the smallest amount of NS-NS flux (“ k = 1”) is shown to be dual to the spacetime CFT given by the large N limit of the free symmetric product orbifold Sym N T 4 . To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS 3 × S 3 part is described by the p s u 1 , 1 | 2 1 WZW model (which is well defined). Unlike the case for k ≥ 2, it turns out that the string spectrum at k = 1 does not exhibit the long string continuum, and perfectly matches with the large N limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.

Abstract Correlation functions of the SL(2,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 [1]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [2] based on the so-called SL(2,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 AdS3/CFT2 holographic duality at finite ’t Hooft coupling.

Abstract We revisit the fermionic string theory onAdS₃× 𝓝with k = 1, and its single-traceTT̅ ̅deformation, with a focus on the (2, 2) superstring on (deformed)AdS₃× 𝕋³. In a certain limit, it is dual to the symmetric product of the (TT̅ ̅-deformed) SCFT2 onℝ× 𝕋³. We present the winding-one delta-function normalizable worldsheet operators which, in the k = 1 decoupling limit, correspond to those ofℝ× 𝕋³in spacetime. We then demonstrate how their properties in string theory reproduce those ofℝ× 𝕋³, or more generally, of a (TT̅ ̅-deformed)ℝ× 𝓝seed of the boundary theory.

A bstract We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold Sym N ( T 4 ). We strengthen the analysis of [ 1 ] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ 3 . We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕ N Sym N ( T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of T 4 and of deforming away from the orbifold by the marginal deformation.

A bstract We consider string theory on AdS 3 × S 3 × 𝕋 4 in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal AdS 3 , the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on thermal AdS 3 and the conical defect with a torus boundary is shown to agree, thus giving evidence for the equivalence of the tensionless string on these different background geometries. We also find that thermal AdS 3 and the BTZ black hole are dual descriptions and the vacuum of the BTZ black hole is mapped to a single long string winding many times asymptotically around thermal AdS 3 . Thus the system yields a concrete example of the string-black hole transition. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. We argue that the same mechanism can lead to a resolution of the factorization problem when geometries with disconnected boundaries are considered, since the connected and disconnected geometries give the same contribution and we do not have to include them separately.

A bstract We study superstring theory in three dimensional Anti-de Sitter spacetime with NS-NS flux, focusing on the case where the radius of curvature is equal to the string length. This corresponds to the critical level k = 1 in the formulation as a Wess-Zumino-Witten model. Previously, it was argued that a transition takes place at this special radius, from a phase dominated by black holes at larger radius to one dominated by long strings at smaller radius. We argue that the infinite tower of modes that become massless at k = 1 is a signal of this transition. We propose a simple two-dimensional conformal field theory as the holographic dual to superstring theory at k = 1. As evidence for our conjecture, we demonstrate that our putative dual exactly reproduces the full spectrum of the long strings of the weakly coupled string theory, including states unprotected by supersymmetry.

A bstract We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.

A bstract We propose a new AdS 3 /CFT 2 duality, in which the bulk string theory has a target spacetime AdS 3 times a squashed three-sphere S ♭ 3 , and the dual CFT 2 is a symmetric product of sigma models on ℝ ϕ × S ♭ 3 , deformed by a ϕ -dependent ℤ 2 twist operator. The duality maps the asymptotic region of AdS 3 to the region ϕ → ∞ , where the twist interaction in the CFT 2 turns off. The AdS 3 backgrounds in question have R AdS < ℓ s , and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS 3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT 2 by a systematic analysis of the worldsheet string theory on AdS 3 .

A bstract We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS 3 × with NS-NS flux and a single-trace deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with , where h is the spacetime conformal weight, is a deformation parameter, p and are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured correspondence.