The sigma model describing the dynamics of the superstring in the $AdS_5 \times S^5$ background can be constructed using the coset $PSU(2,2|4)/SO(4,1)\times SO(5)$. A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE's is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE's. We also compute the OPE's of the left invariant currents with the energy momentum tensor at tree level and one loop.
It is proven that the classical pure spinor superstring in an AdS_5 x S^5 background has a flat current depending on a continuous parameter. This generalizes the recent result of Bena, et al. for the classical Green-Schwarz superstring.
It is proven that the pure spinor superstring in an AdS_5 x S^5 background remains conformally invariant at one loop level in the sigma model perturbation theory.
The tree-level operator product expansion coefficients of the matter currents are calculated in the pure spinor formalism for type IIB superstring in the AdS(5)*S(5) background.
We analyze the anti-de Sitter (AdS) superparticle and superstring systems described in terms of supermatrix valued coordinates proposed by Roiban and Siegel. This approach gives simple symmetry transformations and equations of motion. We examine their kappa-transformations, infinite reducibility and kappa-gauge fixing conditions. A closed first class constraint set for the AdS superparticle is GL(4|4) covariant and keeping superconformal symmetry manifestly. For the AdS superstring $σ$-dependence breaks the GL(4|4) covariance, where supercovariant derivatives and currents satisfy the inhomogen…
The PSU(2,2|4) transformation laws of the IIB superstring theory in the AdS_5 x S^5 background are explicitly obtained for the light-cone gauge in the Green-Schwarz formalism.
In this paper we study the pure spinor formulation of the superstring in $AdS_5\times S^5$ around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background.
We find a new sector of string theory in AdS_5xS^5 describing non-relativistic superstrings in that geometry. The worldsheet theory of non-relativistic strings in AdS_5xS^5 is derived and shown to reduce to a supersymmetric free field theory in AdS_2. Non-relativistic string theory provides a new calculable setting in which to study holography.
We consider the AdS_5 x S^5 superstring in the light-cone gauge adapted to a massless geodesic in AdS5 in the Poincare patch. The resulting action has a relatively simple structure which makes it a natural starting point for various perturbative quantum computations. We illustrate the utility of this AdS light-cone gauge action by computing the 1-loop and 2-loop corrections to the null cusp anomalous dimension reproducing in a much simpler and efficient way earlier results obtained in conformal gauge. This leads to a further insight into the structure of the superstring partition function in n…
An integrable deformation of the type IIB AdS_5 x S^5 superstring action is presented. The deformed field equations, Lax connection, and kappa-symmetry transformations are given. The original psu(2,2|4) symmetry is expected to become q-deformed.
The duality between the type IIB superstring theory in an $AdS_5 \times S^5$ background with $N$ units of five-form flux and ${\cal N} =4$ super Yang--Mills theory with a $U(N)$ gauge group has been studied extensively. My version of the construction of the superstring world-sheet action is reviewed here. This paper is dedicated to Michael Duff on the occasion of his 70th birthday.
We review the spinor moving frame formulations and generalized action principle for super-p-branes, describe in detail the superembedding approach to superstring in general type IIB supergravity background and present the complete superembedding description of type IIB superstring in the AdS(5)xS*5 superspace.
We study superstring theories on AdS(3) x N backgrounds yielding N=2,3,4 extended superconformal symmetries in the dual boundary CFT. In each case the necessary constraints on the internal worldsheet theory N are found.
The Poisson algebra of the Lax matrix associated with the Pohlmeyer reduction of the AdS_5 x S^5 superstring is computed from first principles. The resulting non-ultralocality is mild, which enables to write down a corresponding lattice Poisson algebra.
We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both bosonic and fermionic fields.
We present the construction of the $λ$-deformation of $AdS_5\times S^5$ superstring from the four dimensional Chern-Simons-type gauge theory. The procedure is applicable to all the semi-symmetric coset models and generalizes the previous construction of $λ$-deformation of the symmetric coset models.
A quantizable action has recently been proposed for the superstring in an AdS_5 x S^5 background with Ramond-Ramond flux. In this paper, we construct physical vertex operators corresponding to on-shell fluctuations around the AdS_5 x S^5 background. The structure of these AdS_5 x S^5 vertex operators closely resembles the structure of the massless vertex operators in a flat background.
In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the $AdS_5\times S^5$ superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism.
We examine the surface term for the BRST transformation of the open pure spinor superstring in an AdS_5 x S^5 background. We find that the boundary condition to eliminate the surface term leads to a classification of possible configurations of 1/2 supersymmetric D-branes.
We present an integrable deformation of the $AdS_{5}\times S^{5}$ pure spinor action based on homological perturbation theory. Its equations of motion, Lax connection and BRST symmetry are discussed. The resulting model describes a pure spinor superstring in a generalized supergravity background.
It is developed the phase-space formulation for the Type IIA superstring on the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which the light-like directions are taken from the D=3 Minkowski boundary of AdS_4. After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.
Using the pure spinor formalism for the superstring in an $AdS_5\times S^5$ background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states.
We review the Pohlmeyer reduction procedure of the superstring sigma model on AdS_n x S^n leading to a gauged WZW model with an integrable potential coupled to 2d fermions. In particular, we consider the case of the Green-Schwarz superstring on AdS_3 x S^3 supported by RR flux. The bosonic part of the reduced model is given by the sum of the complex sine-Gordon Lagrangian and its sinh-Gordon counterpart. We determine the corresponding fermionic part and discuss possible existence of hidden 2d supersymmetry in the reduced action. We also elaborate on some general aspects of the Pohlmeyer reduct…
The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.
Green-Schwarz action of Type IIB string on $AdS_3 \times S^3$ is constructed via coset superspace approach. The construction relies exclusively on symplectically Majorana-Weyl spinor formalism, thus permitting it easier to prove $κ$-symmetry for on-shell Type IIB supergravity backgrounds.
We consider fixing the bosonic light-cone gauge for string in AdS in the phase space framework, i.e. by choosing $x^+ = τ$, and by choosing $σ$ so that $P^+$ is distributed uniformly (its density is independent of $σ$). We discuss classical bosonic string in AdS space and superstring in AdS_5 x S^5. In the latter case the starting point is the action found in hep-th/0007036 where the kappa-symmetry is fixed by a fermionic light cone gauge. We derive the light cone Hamiltonian in the AdS_5 x S^5 case and in the case of superstring in AdS_3 x S^3. We also obtain a realization of the generators o…
The super 0-brane and GS superstring actions on AdS$_2 \times S^2$ background with 2-form flux are constructed by supercoset approach. We find the super 0-brane action contains two parameters which are interpreted as the electric and magnetic charges of the super 0-brane. The obtained super 0-brane action describes the BPS saturated dyonic superparticle moving on AdS$_2 \times S^2$ background. The WZ action contains the required coupling with 2-form flux. For GS superstring, we find the string action on AdS$_2 \times S^2$ takes the same form as those in AdS$_3 \times S^3$ and AdS$_5 \times S^5…
It is proved that when 8 fermions associated with the supersymmetries broken by the AdS_4 x CP^3 superbackground are gauged away by using the kappa-symmetry corresponding equations obtained by variation of the AdS_4 x CP^3 superstring action are contained in the set of fermionic equations of the OSp(4|6)/(SO(1,3) x U(3)) sigma-model.
We examine a bilinear form Wess-Zumino term for a superstring in anti-de Sitter (AdS) spaces. This is composed of two parts; a bilinear term in superinvariant currents and a total derivative bilinear term which is required for the pseudo-superinvariance of the Wess-Zumino term. The covariant supercharge commutator containing a string charge is also obtained.
We construct the covariant kappa-symmetric superstring action for a type IIB superstring on AdS_5 x S^5 background. The action is defined as a 2d sigma-model on the coset superspace SU(2,2|4) / SO(4,1) x SO(5) and is shown to be the unique one that has the correct bosonic and flat space limits.
Non-supersymmetric d=4 gauge theories which arise from superstring duality on a manifold $AdS_5 \times S_5/Z_p$ are cataloged for a range $2 \leq p \leq 41$. A number have vanishing two-loop gauge β-function, a necessary but not sufficient condition to be a conformal field theory.
We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present Part I deals with foundations of classical string theory in AdS_5 x S^5, light-cone perturbative quantization and derivation of the exact light-cone world-sheet scattering matrix.
We consider the open superstring action in the AdS$_4 \times \mathbf{CP}^3$ background and investigate the suitable boundary conditions for the open superstring describing the 1/2-BPS D-branes by imposing the $κ$-symmetry of the action. This results in the classification of 1/2-BPS D-branes from covariant open superstring. It is shown that the 1/2-BPS D-brane configurations are restricted considerably by the Kähler structure on $\mathbf{CP}^3$. We just consider D-branes without worldvolume fluxes.
We compute the one-loop world-sheet correction to partition function of $AdS_5 \times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2π(1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is differ…
We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description.
We consider the AdS_4 x CP^3 IIA superstring sigma-model in the background of the "spinning string" classical solution, which possesses two Noether spins. In the limit when one of the spins is infinite there are massless excitations, which govern the infrared worldsheet properties of the model. We obtain a sigma-model of CP^3 with fermions, which describes the dynamics of these massless modes.
We consider three-parameter Yang-Baxter deformations of the $AdS_5\times T^{1,1}$ superstring for abelian $r$-matrices which are solutions of the classical Yang-Baxter equation. We find two new backgrounds which are dual to the dipole deformed Klebanov-Witten gauge theory and to the nonrelativistic Klebanov-Witten gauge theory with Schrödinger symmetry
We briefly review a covariant analysis of D-branes of type IIB superstring on the AdS_5xS^5 background from the κ-invariance of the Green-Schwarz string action. The possible configurations of D-branes preserving half of supersymmetries are classified in both cases of AdS_5xS^5 and the pp-wave background.
Some properties of N=2 superstrings on AdS_3 x N are studied. Their spectrum has the same pattern as 2-d CFTs in the moduli space of symmetric products M^p/S_p, where p is associated with the number of long fundamental strings required to construct the AdS_3 background, and M is the spacetime CFT corresponding to short string excitations of a single long string. Worldsheet operators associated with w long strings correspond to twisted sectors of M^p/S_p.
We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S(5). While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first vs second derivative kinetic terms, presence vs absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of sixteen fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring …
We construct the action for the pure spinor superstring in the coset description of AdS_4 x CP^3 superspace, using the variables which solve the pure spinor condition. As a test of the consistency of the approach, we use the background field method to verify the absence of central charge at the second order in the expansion and to show the one-loop finiteness of the effective action.
We construct the Lax connection of the Green-Schwarz superstring in AdS_5 x S^5 within the Hamiltonian formalism and obtain precisely that used in 0810.4136. It differs in a crucial way from the Bena-Polchinski-Roiban connection by terms proportional to the Hamiltonian constraints. These extra terms ensure firstly that the integrals of motion are all first class and secondly that the Lax connection is flat in the strong sense.
The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on $AdS_5\otimes S^5$ have been pointed out by Bena et al. In this paper, we shown that the Hodge dual between the Maurer-Cartan equation and the equation of motion gives the hidden symmetry in the moduli space of Green-Schwarz superstring. Thus by twisty transforming the vielbeins, we can express the currents of the paper$^{\cite{bpr}}$ as the Lax connections by a unique spectral parameter.
Using the pure spinor formalism, a particular superstring scattering amplitude involving one closed string and $N$ open string vertex operators in $\mathrm{AdS}{}_5 \times \mathrm{S}^5$ is studied. It is shown that the tree-level amplitude containing one supergravity state and $N$ super-Yang-Mills states located on D3-branes near the AdS${}_5$ boundary can be expressed as a $d=4$ ${\cal N}=4$ harmonic superspace integral in terms of the supergravity and super-Yang-Mills superfields.
We consider the open superstring action in AdS_5 x S^5 background with the bilinear Wess-Zumino term, which has been modified in such a way that a certain total derivative term is absent, and give the covariant description of supersymmetric D-branes. We show that the modification of bilinear Wess-Zumino term is necessary to describe correctly the 1/2-BPS D(-1)-brane in AdS_5 x S^5 background, while the classification of other supersymmetric D-branes does not depend on such modification.
We propose an action for a sine-Gordon-like theory, which reproduces the classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring on AdS(5) x S(5). The action is relativistically invariant. It is a mass-deformed gauged WZW model for SO(4,1) x SO(5) / SO(4) x SO(4) interacting with fermions.
Following hep-th/0001204 we discuss the computation of quantum corrections near long IIB superstring configurations in AdS_5 x S^5 which are related to the Wilson loop expectation values in the strong coupling expansion of the dual n=4 SYM theory with large N. We use the Green-Schwarz description of superstrings in curved R-R backgrounds and demonstrate that it is well-defined and useful for developing perturbation theory near long string backgrounds.
We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.
We describe the type IIB supergravity background on AdS_{5} X S_{5} using the potentials of AdS_{5|4} X S_{5} and we use the supersolvable algebra associated to AdS_{5|4} to compute the k gauge fixed type IIB string action.
We generalize the initial steps of the Faddeev-Reshetikhin procedure to the AdS_5 x S^5 superstring theory. Specifically, we propose a modification of the Poisson bracket whose alleviated non-ultralocality enables to write down a lattice algebra for the Lax matrix. We then show that the dynamics of the Pohlmeyer reduction of the AdS_5 x S^5 superstring can be naturally reproduced with respect to this modified Poisson bracket. This work generalizes the alleviation procedure recently developed for symmetric space sigma-models. It also shows that the lattice algebra recently obtained for the AdS_…
Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS_5 x S^5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.
We construct infinite number of conserved nonlocal charges for type IIB superstring on the AdS5xS5 space in the conformal gauge without assuming any kappa gauge fixing, and show that they satisfy the super Yangian algebra. The resultant algebra is the same as our previous work, where a special gauge was assumed in such a way that the Noether current satisfies a flatness condition. However the flatness condition for the Noether current of a superstring on the AdS space is broken in general. We show that the anomalous contribution is absorbed into the current where fermionic constraints play an …
We study the hybrid formulation of Green-Schwarz superstrings on AdS_3 with NS flux and the boundary N=4 superconformal algebra. We show the equivalence between the NSR and GS superstrings by a field redefinition. The boundary N=4 superconformal algebra is realized by the free fields of the affine Lie superalgebra A(1|1)^{(1)}. We also consider the light-cone gauge and obtain the N=4 super-Liouville theory which describes the effective theory of the single long string near the singularities of the D1-D5 system.
We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on $AdS_3\times S^3 \times T^4$ with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.
Superstrings propagating on backgrounds of the form AdS_3 x G/H are studied using the coset CFT approach. We focus on seven dimensional cosets which have a semiclassical limit, and which give rise to N=3 superconformal symmetry in the dual CFT. This is realized for the two cases AdS_3 x SU(3)/U(1) and AdS_3 x SO(5)/SO(3), for which we present an explicit construction. We also provide sufficient conditions on a CFT background to enable a similar construction, and comment on the geometrical interpretation of our results.
We consider D-branes of open superstrings in the AdS_5 x S^5 background. The possible configurations of D-branes preserving half of supersymmetries are classified by analyzing the kappa-invariance of an open superstring in a covariant manner. We also revisit the classification of D-branes in the pp-wave background. It is shown that Penrose limits of the possible D-branes in the AdS_5 x S^5 give all of the D-branes in the pp-wave. In addition, 1/4 supersymmetric D-string, which is related to the D-string preserving 8 dynamical supersymmetries in the pp-wave, is presented. We also discuss the re…
We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 supers…
This is a comprehensive review of the worldsheet techniques for the quantization of type IIB superstring theory on the AdS_5 x S^5 background, using the pure spinor formalism. Particular emphasis is devoted to AdS/CFT applications, with several examples worked out in details. The review is self-contained and pedagogical. Table of contents: 1) Introduction; 2) Generalities; 3) Supercoset sigma models; 4) Quantum effective action and conformal invariance; 5) String spectrum; 6) Integrability.
We discuss manifestly SL(2,C)x SU(4) and kappa invariant superstring action in AdS(5) x S(5) background in the framework of Green-Schwarz formulation. The action is formulated in terms of 16 Poincare fermionic coordinates which through AdS/CFT correspondence should represent N=4 SYM superspace and 16 superconformal fermionic coordinates. The action is also manifestly invariant with respect to the usual N=4 Poincare superalgebra transformations. kappa-symmetry gauge fixing and the derivation of light-cone gauge action is simplified.
