In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through alternative arguments using dynamical supersymmetries. We show that by using the susy algebra the same quantum definition of the energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi identities we indirectly compute the Virasoro anomaly terms by calculating second order susy variation of the EM tensor. Certain integrated form of all such terms are shown to vanish. In order to deal with various divergences that appear in such computations we take a point-split definition of the same EM tensor. The final results are shown not to suffer from the ordering ambiguity as noticed in the previous work provided the coincidence limit is taken before sending the regularization parameter to zero at the end of the computation.
We clarify the relation between the vertex operators in type IIB matrix model and superstring. Green-Schwarz light-cone closed superstring theory is obtained from IIB matrix model on two dimensional noncommutative backgrounds. Superstring vertex operators should be reproduced from those of IIB matrix model through this connection. Indeed, we confirm that supergravity vertex operators in IIB matrix model on the two dimensional backgrounds reduce to those in superstring theory. Noncommutativity plays an important role in our identification. Through this correspondence, we can reproduce superstri…
We show that the super D-string action is canonically equivalent to the type IIB superstring action with a world-sheet gauge field. Canonical transformation to the type IIB theory with dynamical tension is also constructed to establish the SL(2,Z) covariance beyond the semi-classical approximations.
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.
We discuss properties of D-brane configurations in the matrix model of type IIB superstring recently proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya. We calculate central charges in supersymmetry algebra at infinite N and associate them with one- and five-branes present in IIB superstring theory. We consider classical solutions associated with static three- and five-branes and calculate their interactions at one loop in the matrix model. We discuss some aspects of the matrix-model formulation of IIB superstring.
We investigate the NBI matrix model with the potential $XΛ+X^{-1}+(2η+1)\log X$ recently proposed to describe IIB superstrings. With the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich matrix model for $η\ne0$ and find the explicit transformation between the two models.
We obtain a family of type IIB superstring backgrounds involving Ramond-Ramond fields in ten dimensions starting from a heterotic string background with vanishing gauge fields. To this end the global $SL(2,R)$ symmetry of the type IIB equations of motion is implemented as a solution generating transformation. Using a geometrical analysis we show that the type IIB backgrounds obtained are solutions to all orders in $α^{\prime}$.
We quantize the type IIB GS string action on AdS3 X S3 with pure NSNS background and we show that it is equivalent to Liouville with periodic boundary condition plus free spacetime fermions.
We construct Green-Schwarz (GS) light-cone closed superstring theory from type IIB matrix model. A GS light-cone string action is derived from two dimensional N=8 U(n) noncommutative Yang-Mills (NCYM) by identifying noncommutative scale with string scale. Supersymmetry transformation for the light-cone gauge action is also derived from supersymmetry transformation for IIB matrix model. By identifying the physical states and interaction vertices, string theory is perturbatively reproduced.
We recast the result of our recent computation of the quartic action of ten-dimensional IIB supergravity in a manifestly SL(2,R)-covariant form. This affords us a critical assessment of an earlier conjecture in the literature.
A family of type IIB superstring backgrounds involving Ramond-Ramond fields are obtained in ten dimensions starting from a K-model through a generalization of our recent results. The unbroken global $SL(2,R)$ symmetry of the type IIB equations of motion are implemented in this context as a solution generating transfromation. A geometrical analysis, based on the tensor structure of the higher order $α^{\prime}$ terms in the equations of motion, is employed to show that these backgrounds are exact.
I review the properties of a matrix action of relevance for IIB superstrings. This model generalizes the action proposed by Ishibashi, Kawai, Kitazawa, and Tsuchiya by introducing an auxillary field Y, which is the matrix version of the auxillary field g in the Schild action.
In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts $λ$ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superst…
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.
We construct the covariant $κ$-symmetric superstring action for type $IIB$ superstring on plane wave space supported by Ramond-Ramond background. The action is defined as a 2d sigma-model on the coset superspace. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz superstring action and find the light-cone string Lagrangian and the Hamiltonian. The resulting light-cone gauge action is quadratic in both the bosonic and fermionic superstring 2d fields, and therefore, this model can be explicitly quantized. We also obtain a realization of the generators of the basic …
We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This happens at the saddle point for the Yang-Mills field. It turns out that the large-n limit in this matrix model corresponds to a double scaling limit in the Penner model.
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 show that the super D-string action is exactly equivalent to the IIB Green-Schwarz superstring action with some "theta term" in terms of the path integral. Since the "theta term" imposes the Gauss law constraint on the physical state but contributes to neither the mass operator nor the constraints associated with the kappa symmetry and the reparametrization, this exact equivalence implies that the impossibility to disentangle the first and second class fermionic constraints covariantly in the super D-string action is generally inherited from the IIB Green-Schwarz superstring action except s…
A geometrical approach in the non-symmetric connection framework is employed to examine the issue of higher order $α'$ corrections to D=10 type IIB superstring backgrounds with a covariantly constant null Killing isometry and non-zero Ramond-Ramond field content. These describe generalized supersymmetric string waves and were obtained recently by us through the S-duality transformation of purely NS-NS plane wave backgrounds. We find that the backgrounds are exact subject to the existence of certain field redefinitions and provided certain restrictive conditions are satisfied.
D-brane actions depend on a world-volume abelian vector field and are described by Born-Infeld-type actions. We consider the vector field duality transformations of these actions. Like the usual 2d scalar duality rotations of isometric string coordinates imply target space T-duality, this vector duality is intimately connected with SL(2,Z)-symmetry of type IIB superstring theory. We find that in parallel with generalised 4-dimensional Born-Infeld action, the action of 3-brane of type IIB theory is SL(2,Z) self-dual. This indicates that 3-brane should play a special role in type IIB theory and …
On-shell superspace techniques are used to quantify R-symmetry violation in type IIB superstring theory amplitudes in a flat background in ten dimensions. This shows the existence of a particularly simple class of non-vanishing amplitudes in this theory which violate R-symmetry maximally. General properties of the class and some of its extensions are established which at string tree level are shown to determine the first three non-trivial effective field theory contributions to all multiplicity. This leads to a natural conjecture for the exact analytic part of the first two of these.
A natural SL(2,Z) invariant generalization of the Veneziano amplitude in type IIB superstring theory is investigated. It includes certain perturbative and non-perturbative (D-instanton) contributions, and it reduces to the correct expressions in different limits. The singularities are poles in the $s$-$t$-$u$ channels, corresponding to the exchange of particles with a mass spectrum coinciding with that of $(p,q)$ string states. We describe the general structure of the associated perturbative corrections to the effective action.
We analyze the interaction between the massless RR states with a dilaton in a type IIB superstring. By constructing vertex operators for massless and massive RR states and computing their correlation functions with a dilaton we find the Ramond-Ramond part of the superstring low-energy effective action. The RR terms appearing in the action do not contain the standard dilatonic factor (string coupling constant). The geometrical interpretation of this fact is presented. Namely we argue that the spin operators in the RR vertices effectively decrease the Euler character of the worldsheet by 1 unit.…
We address the problem of a non-perturbative formulation of superstring theory by means of the recently proposed matrix models. For the model by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT), we perform one-loop calculation of the interaction between operator-like solutions identified with D-brane configurations of type IIB superstring (in particular, for parallel moving and rotated static p-branes). Comparing to the superstring calculations, we show that the matrix model reproduces the superstring results only at large distances or small velocities, corresponding to keeping only the lowest m…
We solve the tensionless string in a constant plane wave background and obtain a hugely degenerate spectrum. This is the case for a large class of plane wave backgrounds. We show that the solution can also be derived as a consistent limit of the quantized tensile theory of IIB strings in a pp-wave. This is in contrast to the situation for several other backgrounds.
We propose a four-point effective action for the graviton, antisymmetric two-forms, dilaton and axion of type IIB superstring in ten dimensions. It is explicitly SL(2,Z)-invariant and reproduces the known tree-level results. Perturbatively, it has only one-loop corrections for the NS-NS sector, generalizing the non-renormalization theorem of the R^4 term. Finally, the non-perturbative corrections are of the expected form, namely, they can be interpreted as arising from single D-instantons of multiple charge.
We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.
An SL(2, Z) family of string solutions of type IIB supergravity in ten dimensions is constructed. The solutions are labeled by a pair of relatively prime integers, which characterize charges of the three-form field strengths. The string tensions depend on these charges in an SL(2, Z) covariant way. Compactifying on a circle and identifying with eleven-dimensional supergravity compactified on a torus implies that the modulus of the IIB theory should be equated to the modular parameter of the torus.
The SL(2,R) invaraint ten dimensional type IIB superstring effective action is compactified on a torus to D spacetime dimensions. The transformation properties of scalar, vector and tensor fields, appearing after the dimensional reduction, are obtained in order to maintain the SL(2,R)} invariance of the reduced effective action. The symmetry of the action enables one to generate new string vacua from known configurations. As illustrative examples, new black hole solutions are obtained in five and four dimensions from a given set of solutions of the equations of motion.
We describe the type IIB supergravity background on AdS_{3} x S_{3} x T^{4} using the potentials of AdS_{3|4} x S_{3} x T^{4} and we use the supersolvable algebra associated to AdS_{3|4} to compute the kappa gauge fixed type IIB string action. From the explicit form of the action we can clearly see how passing from pure NSNS backgrounds to pure RR backgrounds the WZW term disappears.
We construct the thermal boundary states from the type IIB Green-Schwarz superstring in {\em pp}-wave background in the light-cone gauge. The superstring is treated in the canonical ensemble and in the TFD formalism which is appropriate to discuss quantum systems in the canonical quantization. The thermal boundary states are obtained by thermalizing the total boundary states which are the boundary states of the total system that is composed by the superstring modes and the corresponding thermal reservoir modes. That analysis is similar to the one in the flat spacetime case \cite{ivv12}. Howeve…
We consider type IIB superstring theory with embedded $D5$-brane and choose boundary conditions which preserve half of the initial supersymmetry. In the canonical approach that we use, boundary conditions are treated as canonical constraints. The effective theory, obtained from the initial one on the solution of boundary conditions, has the form of the type I superstring theory with embedded $D5$-brane. We obtain the expressions for $D5$-brane background fields of type I theory in terms of the $D5$-brane background fields of type IIB theory. We show that beside known $Ω$ even fields, they cont…
We reconsider the two-point string scattering amplitudes of massless Neveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theory on the disk and projective plane in ten dimensions and analyse its $α'$ expansion. We also discuss the unoriented Type IIB theory on $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scattering amplitudes of the complex Kähler moduli and complex structures of the untwisted sector are computed on the disk and projective plane. New results are obtained together with known ones. Finally, we compare string scattering amplitudes results at $α'…
We show that the M-theory/IIA and IIA/IIB superstring dualities together with the diffeomorphism invariance of the underlying theories require the presence of certain p-brane bound states in IIA and IIB superstring theories preserving 1/2 of the spacetime supersymmetry. We then confirm the existence of IIA and IIB supergravity solutions having the appropriate p-brane bound states interpretation.
We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large--$N$ limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, possibly is irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.
In this article we investigate the relation between consequences of Dirichlet boundary conditions (momenta noncommutativity and parameters of the effective theory) and background fields of fermionic T-dual theory. We impose Dirichlet boundary conditions on the endpoints of the open string propagating in background of type IIB superstring theory with constant background fields. We showed that on the solution of the boundary conditions the momenta become noncommutative, while the coordinates commute. Fermionic T-duality is also introduced and its relation to noncommutativity is considered. We us…
We derive Schwinger-Dyson equations for the Wilson loops of a type IIB matrix model. Superstring coordinates are introduced through the construction of the loop space. We show that the continuum limit of the loop equation reproduces the light-cone superstring field theory of type IIB superstring in the large-N limit. We find that the interacting string theory can be obtained in the double scaling limit as it is expected.
We examine the dual correspondence between holographic IIB superstring theory and N=4 super Yang-Mills theory at finite values of the coupling constants. In particular we analyze a field theory strong-coupling expansion which is the S-dual of the planar expansion. This expansion arises naturally as the AdS/CFT dual of the IIB superstring scattering amplitudes given a genus truncation property due to modular invariance. The space-time structure of the contributions to the field theory four-point correlation functions obtained from the IIB scattering elements is investigated in the example of th…
The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group $SO(d,d)$ of the vector bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7-manifolds with two covariantly constant spinors leads to a generalised $G_2$-structure associated with a reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU(3)-structure associated with $SU(3)\times SU(3)$, and show how these relate to ge…
We show that the supersymmetric Wilson loops in IIB matrix model give a transition operator from reduced supersymmetric Yang-Mills theory to supersymmetric space-time theory. In comparison with Green-Schwarz superstring we identify the supersymmetric Wilson loops with the asymptotic states of IIB superstring. It is pointed out that the supersymmetry transformation law of the Wilson loops is the inverse of that for the vertex operators of massless modes in the U(N) open superstring with Dirichlet boundary condition.
We rewrite the SL(2,Z) covariant worldsheet action for the IIB string proposed by Townsend in a Polyakov form. In a flat background the formalism yields separate (p,q) sectors. In each one the action is that of the IIB string action with the string slope parameter \alp\pr replaced by its SL(2,Z) analogue \alp_{pq}\pr. SL(2,Z) invariant graviton scattering amplitudes are obtained from those of the fundamental (1,0) string by summing over the different sectors. The tree-level four-graviton amplitude in this formalism differs from a previously conjectured non-perturbative form; both yield the sam…
We propose an explanation via string theory of the correspondence between the Coulomb branch of certain three-dimensional supersymmetric gauge theories and certain moduli spaces of magnetic monopoles. The same construction also gives an explanation, via $SL(2,\Z)$ duality of Type IIB superstrings, of the recently discovered ``mirror symmetry'' in three dimensions. New phase transitions in three dimensions as well as new infrared fixed points and even new coupling constants not present in the known Lagrangians are predicted from the string theory construction. An important role in the construct…
A new procedure was recently proposed for constructing massless Type IIB vertex operators in the pure spinor formalism. Instead of expressing these closed string vertex operators as left-right products of open string vertex operators, they were instead constructed from the complex N=2 d=10 superfield whose lowest real and imaginary components are the dilaton and Ramond-Ramond axion. These Type IIB vertex operators take a simple form in the -8 picture and are related to the usual vertex operators in the zero picture by acting with picture-raising operators. In this paper, we compute explicitly …
S and U-duality dictate that graviton scattering amplitudes in IIB superstring theory be automorphic functions on the appropriate fundamental domain which describe the inequivalent vacua of (compactified) theories. A constrained functional form of graviton scattering is proposed using Eisenstein series and their generalizations compatible with: a) two-loop supergravity, b) genus one superstring theory, c) the perturbative coupling dependence of the superstring, and d) with the unitarity structure of the massless modes. The form has a perturbative truncation in the genus expansion at a given or…
AdS/CFT predicts that the value of the on-shell action for type IIB Supergravity (SUGRA) on $AdS_5 \times S^5$ background must be a non-zero number completely determined from the boundary theory. We examine this statement within Sen's formalism for type IIB SUGRA and find that consistency with AdS/CFT requires us to add a specific boundary term to the action. We contrast our resolution with two other resolutions recently proposed in the literature in the context of different approaches to type IIB SUGRA. We explain how our resolution presents a strong benchmark for the possible boundary term o…
Instanton and seven-brane solutions of type IIB supergravity carrying charges in the Ramond-Ramond sector are constructed. The singular seven-brane has a quantized \RR \ \lq magnetic' charge whereas its dual is the instanton, which is non-singular in the string frame and has an associated {\it global} \lq electric' charge. The product of these charges is constrained by a Dirac quantization condition. The instanton has the form of a space-time wormhole in the string frame, and is responsible for the non-conservation of the Noether current.
In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, which turns to be the $\mathbb{CP}^{3}$ conformal affine Toda model. We review how the position $μ$ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $μ$ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal s…
The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 ba…
Previous studies of the type IIB superstring in an ${AdS_5 \times S^5}$ background are based on a description of the superspace geometry as the quotient space $PSU(2,2|4)/SO(4,1) \times SO(5)$. This paper develops an alternative approach in which the Grassmann coordinates provide a nonlinear realization of $PSU(2,2|4)$ based on the quotient space $PSU(2,2|4)/SU(2,2) \times SU(4)$, and the bosonic coordinates are described as a submanifold of $SU(2,2) \times SU(4)$. This formulation keeps all bosonic symmetries manifest, and it provides the complete dependence on the Grassmann coordinates in te…
We point out that off-shell four-dimensional supersymmetry implies strange hermiticity properties for the N=1 RNS superstring. However, these hermiticity properties become natural when the N=1 superstring is embedded into an N=2 superstring.
We consider random superstrings of type IIB in $d$-dimensional space. The discretized action is constructed from the supersymetric matrix model, which has been proposed as a constructive definition of superstring theory. Our action is invariant under the local N=2 super transformations, and doesn't have any redundant fermionic degrees of freedom.
The continuous and discrete symmetries of a dimensionally reduced type IIB superstring action are employed to generate four-dimensional cosmological solutions with non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond form-fields from the dilaton-moduli-vacuum solutions.
We establish features of so-called Yangian secret symmetries for AdS3 type IIB superstring backgrounds thus verifying the persistence of such symmetries to this new instance of the AdS/CFT correspondence. Specifically, we find two a priori different classes of secret symmetry generators. One class of generators, anticipated from the previous literature, is more naturally embedded in the algebra governing the integrable scattering problem. The other class of generators is more elusive, and somewhat closer in its form to its higher-dimensional AdS5 counterpart. All of these symmetries respect le…
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.
In this paper, we motivate how the Hodge dual related with S-duality gives the hidden symmetry in the moduli space of IIB string. Utilizing the static $% κ$-symmetric Killing gauge, if we take the Hodge dual of the vierbeins keeping the connection invariant, the duality of Maure-Cartan equations and the equations of motion becomes manifest. Thus by twistly transforming the vierbein, we can express the BPR currents as the Lax connections by a unique spectral parameter. Then we construct the generators of the infinitesimal dressing symmetry, the related symmetric algebra becomes the affine $% gl…
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.
A covariant action for closed D=11 superstring with local $κ$-symmetry and global supersymmetry transformations obeying the algebra $\{Q_α,Q_β\}=CΓ^{μν}P_μn_ν$ is suggested. Physical sector variables of the model and their dynamics exactly coincide with those of the D=10 type IIA Green-Schwarz superstring. It is shown that action of the D=10 type IIA Green-Schwarz superstring can be considered as a partially gauge fixed version of the D=11 superstring action.
