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The symmetric orbifold of 핋4 is exactly dual to string theory on AdS3 × S3 × 핋4 with minimal (k = 1) NS-NS flux. In this paper we study the perturbation of the symmetric orbifold that is dual to switching on R-R flux, and hence to deforming the theory away from the tensionless point. More specifically, we determine systematically the action of a centrally extended supersymmetry algebra on the CFT states, and deduce from it the anomalous conformal dimensions. In the w-twisted sector with large w the structure is similar to what was found for N = 4 SYM: the basic excitations are multi-magnons whose individual dispersion relation is fixed by symmetry, and the comparison with the BMN answer suggests that the result is true to all orders in perturbation theory. Finally we show that the multi-magnon states interact via an integrable S-matrix and possess a natural family of bound states. [ABSTRACT FROM AUTHOR]

WZW models based on super Lie algebras play an important role for the description of string theory on AdS spaces. In particular, for the case of AdS 3 × S 3 with pure NS–NS flux the super Lie algebra of psu (1 , 1 | 2) k appears in the hybrid formalism, and higher dimensional AdS spaces can be described in terms of related supergroup cosets. In this paper we study the WZW models based on u (2 | 2) 1 and psu (2 | 2) 1 that may play a role for the worldsheet theory that is dual to free super Yang–Mills in 4D. [ABSTRACT FROM AUTHOR]

The bound state of one NS5 brane (wrapped on a 핋4) and N NS1-branes has two dual descriptions: its low-energy dynamics is described by the symmetric orbifold of 핋4, while the near horizon geometry is captured by string theory on AdS3 × S3 × 핋4 with one unit of NS flux. The latter theory is exactly solvable in the hybrid formalism, and this allows one to prove the equivalence of the two descriptions. In this paper we extend this duality to ℤk orbifolds of this AdS3 × S3 background. In particular, we show that the corresponding worldsheet spectrum reproduces exactly the perturbative excitations on top of a certain non-perturbative state in the dual symmetric orbifold theory. Since the AdS/CFT duality map is exact for these models, we obtain an interesting picture of how the duality relates boundary and bulk descriptions. [ABSTRACT FROM AUTHOR]

The symmetric orbifold of 핋4 is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in AdS3 × S3 × 핋4. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the 2-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective. [ABSTRACT FROM AUTHOR]

For a special family of 4d N = 2 superconformal quiver theories, the worldsheet dual corresponding to the free theory is identified. This result is obtained from the recently proposed worldsheet dual of free N = 4 SYM by applying a ℤk orbifold. In support of our proposal we show that the spectrum of both the untwisted as well as the twisted sectors coincides between the two descriptions. [ABSTRACT FROM AUTHOR]

The BPS correlators of the symmetric product orbifold SymN(핋4) are reproduced from the dual worldsheet theory describing strings on AdS3× S3× 핋4 with minimal (k = 1) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet. [ABSTRACT FROM AUTHOR]

String theory on AdS3× S3× 핋4 with minimal k = 1 NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT Sym(핋4), thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk. [ABSTRACT FROM AUTHOR]

The worldsheet string theory dual to free 4d N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet. [ABSTRACT FROM AUTHOR]

String theory on AdS3 × S3 × T 4 with one unit (k = 1) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at k = 1, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the N = 4 superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW. [ABSTRACT FROM AUTHOR]

String backgrounds of the form 𝕄3× ℳ7 where 𝕄3 denotes 3-dimensional Minkowski space while ℳ7 is a 7-dimensional G2-manifold, are characterised by the property that the world-sheet theory has a Shatashvili-Vafa (SV) chiral algebra. We study the generalisation of this statement to backgrounds where the Minkowski factor 𝕄3 is replaced by AdS3. We argue that in this case the world-sheet theory is characterised by a certain N = 1 superconformal W -algebra that has the same spin spectrum as the SV algebra and also contains a tricritical Ising model N = 1 subalgebra. We determine the allowed representations of this W -algebra, and analyse to which extent the special features of the SV algebra survive this generalisation. [ABSTRACT FROM AUTHOR]

Correlators in symmetric orbifold CFTs are given by a finite sum of admissible branched covers of the 2d spacetime. We consider a Gross-Mende like limit where all operators have large twist, and show that the corresponding branched covers can be described via a Penner-like matrix model. The limiting branched covers are given in terms of the spectral curve for this matrix model, which remarkably turns out to be directly related to the Strebel quadratic differential on the covering space. Interpreting the covering space as the world-sheet of the dual string theory, the spacetime CFT correlator thus has the form of an integral over the entire world-sheet moduli space weighted with a Nambu-Goto-like action. Quite strikingly, at leading order this action can also be written as the absolute value of the Schwarzian of the covering map. Given the equivalence of the symmetric product CFT to tensionless string theory on AdS3, this provides an explicit realisation of the underlying mechanism of gauge-string duality originally proposed in [1] and further refined in [2]. [ABSTRACT FROM AUTHOR]

We employ the free field realisation of the psu 1 1 2 1 world-sheet theory to constrain the correlators of string theory on AdS3× S3× 핋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases. [ABSTRACT FROM AUTHOR]

The symmetric orbifold of is the CFT dual of string theory on with minimal NS–NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation parameter. This suggests that the symmetric orbifold is (at least locally) the most symmetrical CFT in its moduli space. [ABSTRACT FROM AUTHOR]

It was recently argued that string theory on AdS3× S3× 핋4 with one unit (k = 1) of NS-NS flux is exactly dual to the symmetric orbifold CFT SymN (핋4). In this paper we show how to directly relate the n-point correlators of the two sides to one another. In particular, we argue that the correlators of the world-sheet theory are delta-function- localised in string moduli space to those configurations that allow for a holomorphic covering map of the S2-boundary of AdS3 by the world-sheet. This striking feature can be seen both from a careful Ward identity analysis, as well as from semi-classically exact AdS3 solutions that are pinned to the boundary. The world-sheet correlators therefore have exactly the same structure as in the Lunin-Mathur construction of symmetric orbifold CFT correlators in terms of a covering surface — which now gets identified with the world-sheet. Together with the results of [1-2] this essentially demonstrates how the k = 1 AdS3 string theory becomes equivalent to the spacetime orbifold CFT in the genus expansion. [ABSTRACT FROM AUTHOR]

It was recently shown that string theory on AdS3× S3× T 4 with minimal NS-NS flux (k = 1) is exactly dual to the symmetric orbifold of T 4. Here we show that a similar statement also holds for the Dn orbifolds of these backgrounds that have N = (2, 2) supersymmetry. In this case the CFT dual is the symmetric orbifold of T 4/Dn. [ABSTRACT FROM AUTHOR]

We review the duality relating 2D WN minimal model conformal field theories, in a large-N 't Hooft like limit, to higher spin gravitational theories on AdS3. [ABSTRACT FROM AUTHOR]

We evaluate the partition function of three-dimensional theories of gravity in the quantum regime, where the anti-de Sitter (AdS) radius is Planck scale and the central charge is of order one. The contribution from the AdS vacuum sector can--with certain assumptions--be computed and equals the vacuum character of a minimal model conformai field theory. The torus partition function is given by a sum over geometries which is finite and computable. For generic values of Newton's constant G and the AdS radius ℓ the result has no Hilbert space interpretation, but in certain cases it agrees with the partition function of a known conformai field theory. For example, the partition function of pure Einstein gravity with G = 3ℓ equals that of the Ising model, providing evidence that these theories are dual. We also present somewhat weaker evidence that the three-state and tricritical Potts models are dual to pure higher spin theories of gravity based on SL(3) and E6, respectively. [ABSTRACT FROM AUTHOR]

The most general N=2 superconformal boundary states for the c=3 theory consisting of two (uncompactified) free bosons and fermions are constructed. It is shown that the only N=2 boundary states are the familiar Dirichlet boundary states, as well as the Neumann boundary states with an arbitrary electric field. [Copyright &y& Elsevier]

A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c=-2 triplet theory and the k=-4/3 affine su(2) theory. We also give some brief introduction to the work of Zhu. [ABSTRACT FROM AUTHOR]

A class of D-branes for the type IIB plane-wave background is considered that preserve half the dynamical supersymmetries of the light-cone gauge. The D-branes of this type are the Euclidean (or instantonic) (0,0), (0,4), and (4,0) branes (where (r,s) denotes a brane oriented with r axes in the first four directions transverse to the +, − light-cone, and s axes in the second four directions). Corresponding Lorentzian D-branes are (+,−;0,0), (+,−;0,4), and (+,−;4,0). These are constructed in two ways. The first uses a boundary state formalism which implements appropriate fermionic gluing conditions and the second is based on a direct quantization of the open strings ending on the branes. In distinction to the D-branes considered earlier these have massless world-volume fermions but do not possess kinematical supersymmetries. Cylinder diagrams describing the overlap between a pair of boundary states displaced by some distance are evaluated. The open-string description of this system involves mode frequencies that are, in general, given by irrational solutions to transcendental equations. The closed-string and open-string descriptions are shown to be equivalent by a nontrivial implementation of the S modular transformation. A classical description of the D-instanton (the (0,0) case) in light-cone gauge is also given. [Copyright &y& Elsevier]

: Some of the consequences that follow from the C2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C2 condition has only finitely many n-point functions, and this result is used to prove a version of a conjecture of Nahm, namely that every representation of such a conformal field theory is quasirational. We also show that every such vertex operator algebra is a finite W-algebra, and we give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules. [ABSTRACT FROM AUTHOR]

We consider the asymmetric orbifold that is obtained by acting with T-duality on a 4-torus, together with a shift along an extra circle. The chiral algebra of the resulting theory has non-trivial outer automorphisms that act as permutations on its simple factors. These automorphisms play a crucial role for constructing D-branes that couple to the twisted sector of the orbifold. [Copyright &y& Elsevier]

We consider a natural generalisation of the class of hyperbolic Kac–Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they possess a real principal so(1,2) subalgebra. Our class of algebras include the Lorentzian Kac–Moody algebras that have recently been proposed as symmetries of M-theory and the closed bosonic string. [Copyright &y& Elsevier]

The boundary states for a certain class of WZW models are determined. The models include all modular invariants that are associated to a symmetry of the unextended Dynkin diagram. Explicit formulae for the boundary state coefficients are given in each case, and a number of properties of the corresponding NIM-reps are derived. [Copyright &y& Elsevier]

We propose a worldsheet description for the AdS5×S5 string theory dual to large N, free N=4 supersymmetric Yang-Mills theory in four dimensions. The worldsheet theory is a natural generalization of the recently investigated tensionless string on AdS3×S³×T4. As in the case of AdS3 it has a free field description, with spectrally flowed sectors, and is closely related to an (ambi-)twistor string theory. Here, however, we view it as a critical N=4 (closed) string background. We argue that the corresponding worldsheet gauge constraints reduce the degrees of freedom to a finite number of oscillators (string bits) in each spectrally flowed sector. Imposing a set of residual gauge constraints on this reduced oscillator Fock space then determines the physical spectrum of the string theory. Quite remarkably, we find that this prescription reproduces precisely the entire planar spectrum--of single trace operators--of the free supersymmetric Yang-Mills theory. [ABSTRACT FROM AUTHOR]

For string theory on AdS 3 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 AdS 3 × S 3 × T 4 for generic NS-NS flux is described by the symmetric orbifold of (N = 4 Liouville theory) × T 4. For the case of minimal flux (k = 1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T 4 , thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS × 3 X. [ABSTRACT FROM AUTHOR]

The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective. [ABSTRACT FROM AUTHOR]

The affine Yangian of gl1 is known to be isomorphic to W1+∞, the W-algebra that characterizes the bosonic higher spin — CFT duality. In this paper we propose some of the defining relations of the Yangian that are relevant for the N=2 superconformal version of W1+∞. Our construction is based on the observation that the N=2 superconformal W1+∞ algebra contains two commuting bosonic W1+∞ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. The corresponding affine Yangian can therefore be built up from two affine Yangians of gl1 by adding in generators that transform appropriately. [ABSTRACT FROM AUTHOR]

The spectrum of superstrings on AdS3 × S3 × M4 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 M4 = S3 × S1 and M4 = T4 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 × T4 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. [ABSTRACT FROM AUTHOR]

Recently, string theory on AdS3× S3× 𝕋4 with one unit of NS-NS flux (k = 1) was argued to be exactly dual to the symmetric orbifold of 𝕋 4, and in particular, the full (unprotected) spectrum was matched between the two descriptions. This duality was later extended to the case with higher NS-NS background flux for which the long string sector was argued to be described by the symmetric product orbifold of (N = 4 Liouville) × 𝕋 4. In this paper we study correlation functions for the bosonic analogue of this duality, relating bosonic string theory on AdS3× X to the symmetric orbifold of Liouville × X. More specifically, we show that the low-lying null vectors of Liouville theory correspond to BRST exact states from the worldsheet perspective, and we demonstrate that they give rise to the expected BPZ differential equations for the dual CFT correlators. Since the structure constants of Liouville theory are uniquely fixed by these constraints, this shows that the seed theory of the dual CFT contains indeed the Liouville factor. [ABSTRACT FROM AUTHOR]