According to the recent proposal by Aharony, Bergman, Jafferis and Maldacena the N=6 supersymmetric Chern-Simons theory in three dimensions has a 't Hooft limit whose holographic dual is described by type IIA superstings on AdS_4 x CP^3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS_4 x CP^3 with kappa-symmetry partially fixed can be understood as a coset sigma-model on the same space supplied with a proper Wess-Zumino term. We construct the corresponding sigma-model Lagrangian and show that it is invariant under a local fermionic symmetry which for generic bosonic string configurations allows one to remove 8 out of 24 fermionic degrees of freedom. The remaining 16 fermions together with their bosonic partners should describe the physical content of AdS_4 x CP^3 superstring. As further evidence, we demonstrate that in the plane-wave limit the quadratic action arising from our model reproduces the one emerging from the type IIA superstring. The coset sigma-model is classically integrable which opens up the possibility to investigate its dynamics in a way very similar to the case of AdS_5 x S^5 superstrings.
A formulation recently proposed [arXiv:1506.07706] as an alternative to the usual coset PSU(2,2|4)/USp(2,2)USp(4) for the superspace geometry of the Type IIB superstring on an AdS5xS5 background is shown to be a particular parametrization of this coset. Standard methods can then be applied.
We consider superstring sigma models that are based on coset superspaces G/H in which H arises as the fixed point set of an order-4 automorphism of G. We show by means of twistor theory that the corresponding first-order system, consisting of the Maurer-Cartan equations and the equations of motion, arises from a dimensional reduction of some generalised self-dual Yang-Mills equations in eight dimensions. Such a relationship might help shed light on the explicit construction of solutions to the superstring equations including their hidden symmetry structures and thus on the properties of their …
The double-spinor formalism, proposed by Aisaka and Kazama, provides a basis for the pure-spinor formalism, which allows manifestly super-Poincare covariant quantization of superstrings. We extend it to the case of backgrounds realized by coset superspaces. A general method constructing reparametrization invariant action is given using two concrete examples, the flat space-time and AdS(5)xS(5). We find that it is natural to double not only the spinor coordinates but the whole superspace for describing double-spinor superstrings on such backgrounds. The reparametrization invariant action has lo…
We quantize the superstring on the AdS_2 x S^2 background with Ramond-Ramond flux using a PSU(1,1|2)/U(1) x U(1) sigma model with a WZ term. One-loop conformal invariance of the model is guaranteed by a general mechanism which holds for coset spaces G/H where G is Ricci-flat and H is the invariant locus of a Z_4 automorphism of G. This mechanism gives conformal theories for the PSU(1,1|2) x PSU(2|2)/SU(2) x SU(2) and PSU(2,2|4)/SO(4,1) x SO(5) coset spaces, suggesting our results might be useful for quantizing the superstring on AdS_3 x S^3 and AdS_5 x S^5 backgrounds.
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.
We apply the coset character identities (generalization of Jacobi's abstruse identity) to compact and noncompact Gepner models. In the both cases, we prove that the partition function actually vanishes due to the spacetime supersymmetry. In the case of the compact models and discrete parts of the noncompact models, the partition function includes the expected vanishing factor. But the character identities used to the continuous part of the noncompact models suggest that these models have twice as many supersymmetry as expected. This fact is an evidence for the conjecture that the holographical…
In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained fo…
We discuss solutions of the heterotic string theory which are analogous to bosonic and superstring backgrounds related to coset conformal field theories. A class of exact `left-right symmetric' solutions is obtained by supplementing the metric, antisymmetric tensor and dilaton of the superstring solutions by the gauge field background equal to the generalised Lorentz connection with torsion. As in the superstring case, these backgrounds are $\a'$-independent, i.e. have a `semiclassical' form. The corresponding heterotic string sigma model is obtained from the combination of the (1,0) supersymm…
We compute the complete 1-loop spectrum of anomalous dimensions for the bulk fields of non-linear sigma models on symmetric coset (super)spaces G/H, both with and without world-sheet supersymmetry. In addition, we provide two new methods for the construction of partition functions in the infinite radius limit and demonstrate their efficiency in the case of (super)sphere sigma models. Our results apply to a large number of target spaces including superspheres and superprojective spaces such as the N=2 sigma model on CP(3|4).
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.
In this thesis are presented two aplications of the sigma model for the superstring in the pure spinor formulation. The first aplication concerns the computation of the one-loop conformal invariance for the type II superstring, resulting in equations of motion written in superspace for the background fields coupled to the superstring. The second application is related to the BRST invariance of the heterotic superstring at the quantum level, which allows to find stringy corrections to the ten-dimensional super Yang-Mills/supergravity constraints.
It has been believed for a long time that the tensionless limit of superstring theory can be described by a higher spin gauge theory. Recently, a concrete realization of this idea was proposed via 3d Aharony-Bergman-Jafferis (ABJ) theory with the help of holographic duality. In this note we review our work on finding a similar relation involving 2d coset type models. We start by proposing and examining holographic dualities between 3d higher spin gauge theories with matrix valued fields and the large N limit of 2d coset type models. After that we discuss possible relations to superstring theor…
We include in F-theory, through open Type I F-theory branes (F-branes), string theories with N = 1 supersymmetry, both Type I and heterotic. Type I branes are distinguished from Type II by worldvolume parity projection. The same open Type I branes describe both open Type I superstrings and closed heterotic upon different sectionings from F-branes to worldsheets, while closed Type I superstrings arise from closed Type I branes. (Type II superstrings come from closed Type II branes, as described previously.) F-theory manifests the exceptional-group U-duality symmetry, with all massless bosonic f…
We derive the Green-Schwarz action on AdS_5 x S^5 using an alternate version of the coset superspace construction. By Wick rotations and Lie algebra identifications we bring the coset to GL(4|4)/(Sp(4) x GL(1))^2, which allows us to represent the conformal transformations on unconstrained matrices. The derivation is more streamlined even for the bosonic sector, and conformal symmetry is manifest at every step. Kappa-symmetry gauge fixing is more transparent.
The sigma model action described in this paper differs in four important features from the usual sigma model action for the four-dimensional Green-Schwarz heterotic superstring in a massless background. Firstly, the action is constructed on an N=(2,0) super-worldsheet using a Kahler potential and an Ogievetsky-Sokatchev constraint; secondly, the target-space background fields are unconstrained; thirdly, the target-space dilaton couples to the two-dimensional curvature; and fourthly, the action reduces in a flat background to a free-field action. A conjecture is made for generalizing this N=(2,…
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…
The mathematical framework for an exact quantization of the two-dimensional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous results the two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler-DeWitt equations to solutions of a modified (Coset) Knizhnik-Zamolodch…
The Poisson-Lie (PL) T-duality is a generalized T-duality based on the Lie algebra of the Drinfel'd double. In particular, when we consider the PL T-duality of a coset space, the dual space is found to be a generalized coset space, which is called the dressing coset. In this paper, we investigate an extension of the dressing cosets to the U-duality setup. We propose the gauged actions for various branes in M-theory and type IIB theory, where the generalized metric is constructed by using the Exceptional Drinfel'd Algebra (EDA) and the gauge algebra is a certain isotropic subalgebra of the EDA.…
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 review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G/H$. We discuss a potential impediment, appearing in these models when integrating out the gauge field in favour of the dual variables. This process cannot be performed in general and we isolate the obstruction, highlighting three cases in which a solution can be found. After writing the T-dual action we provide solution for two specific models. The first based on the symmetric space $S^{3} \simeq SO(4)/SO(3)$, well-known in the literature, the second on…
The first-order formulation of the G/K symmetric space sigma model of the scalar cosets of the supergravity theories is discussed when there is coupling of (m-1)-form matter fields. The Lie superalgebra which enables the dualized coset formulation is constructed for a general scalar coset G/K with matter coupling where G is a non-compact real form of a semi-simple Lie group and K is its maximal compact subgroup.
We derive the coherent state representation of the integrable spin chain Hamiltonian with non-compact supersymmetry group G=SU(1,1|1). By passing to the continuous limit, we find a spin chain sigma model describing a string moving on the supercoset G/H, H being the stabilizer group. The action is written in a manifestly G-invariant form in terms of the Cartan forms and the string coordinates in the supercoset. The spin chain sigma model is shown to agree with that following from the Green-Schwarz action describing two-charged string spinning on AdS_5 x S^5.
By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on $3N-2$ free parameters. For $N=1$ the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the $N=2$ case and show that it admits a remarkably simple form in terms of the classical $\mathcal{R}$-matrix underlying the integrability of these models. We conjecture that …
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 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.
The extended supersymmetric (SUSY) sigma-model has been proposed on the bases of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have investigated the SUSY sigma-model on the Kaehler manifold, the coset space SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the potential in the SO(2N)/U(N) coset space to that in the …
This paper considers the Free Differential Algebra and rheonomic parametrization of type IIA Supergravity, extended to include the BRS differential and the ghosts. We consider not only the ghosts lambda's of supersymmetry but also the ghosts corresponding to gauge and Lorentz transformations. In this way we can derive not only the BRS transformations of fields and ghosts but also the standard pure spinor constraints on lambda's. Moreover the formalism allows to derive the action for the pure spinor formulation of type IIA superstrings in a general background, recovering the action first obtain…
The gravity dual of $β$-deformed ABJM theory can be obtained by a TsT transformation of $AdS_4\times\mathbb{CP}^3$. We present a supercoset construction of $\mathbb{CP}^3$ to obtain this gravity dual theory as a Yang-Baxter deformation. This is done by selecting a convenient combination of Cartan generators in order to get an Abelian $r$-matrix satisfying the classical Yang-Baxter equation. Our results provide another illustration of the relation between Abelian $r$-matrices and TsT transformations.
The construction of flat currents, and hence conserved non-local charges, for the superstring on AdS_5 x S^5 is generalised. It is shown that such currents exist for sigma-model type actions on all coset (super-)spaces G/H in which, at the level of the Lie algebras, h is the grade-zero subspace of a Zm grading of g. This is true for an essentially unique choice of the Wess-Zumino term, which is determined.
We consider a 2-d conformal theory based on (G x G')/ H coset sigma model introduced by Guadagnini, Martellini and Mintchev. It is shown that in the case of {SU(2) x SU(2)}/ U(1) the metric of the corresponding background is of T^{p,q} coset space form (but is not an Einstein one). Similar interpretation is possible for the Lorentzian coset space W_{4,2}= {SL(2,R) x SL(2,R)}/U(1). The resulting 10-d homogeneous space metric on W_{4,2} x T^{p,q} supplemented with 2-form field gives a critical NS-NS superstring background with conformal sigma model interpretation.
We derive the torsion constraints and show the consistency of equations of motion of four-dimensional Type II supergravity in superspace, with Type II sigma model. This is achieved by coupling the four-dimensional compactified Type II Berkovits' superstring to an N=2 curved background and requiring that the sigma-model has superconformal invariance at tree-level. We compute this in a manifestly 4D N=2 supersymmetric way. The constraints break the target conformal and SU(2) invariances and the dilaton will be a conformal, $SU(2)\times U(1)$ compensator. For Type II superstring in four dimension…
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.
The Green-Schwarz covariant N=2 superstring action can be consistently deduced as the action of the Wess-Zumino-Witten (WZW) sigma model defined on the direct product of two N=1, D=10 Poincaré supertranslation groups. Generalizing this result, we construct new WZW sigma models on the supergroups with a nonabelian even part and interpret them as models of superstrings moving on the supergroup manifolds. We show that these models are completely integrable and in some special cases possess fermionic kappa-symmetry.
A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime is flat. When the six-dimensional spacetime is $AdS_3\times S^3$, the action reduces to one found earlier with Vafa and Witten.
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 …
A procedure is developed for constructing deformations of integrable sigma-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter sigma-model introduced a few years ago by C. Klimcik. In the case of the symmetric space sigma-model on F/G we obtain a new one-parameter family of integrable sigma-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresp…
We consider integrability properties of the superstring on $AdS_{5}\times S^{5}$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the sigma model action and determine the Poisson algebra of the transition matrices. We reveal the generalization of the $\mathbb{Z}_{4}$ automorphism analogous to the sigma models defined on a symmetric space coset. A possible regularization scheme for the ambiguities present, which respects the generalized automorphism, is also discussed.
We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the correspond…
We consider two integrable deformations of 2d sigma models on supercosets associated with AdS_n x S^n. The first, the "eta-deformation" (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring action on AdS_n x S^n, while the second, the "lambda-deformation" (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the AdS_n x S^n superstring. We show that the eta-deformed model may be obtained from the lambda-deformed one by a special scaling limit and analytic continuation in coordinates combined with a particular …
The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space sigma models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to sym…
The oxidation program of hep-th/0210178 is extended to cover oxidation of 3-d sigma model theories on a coset G/H, with G non-compact (but not necessarily split), and H the maximal compact subgroup. We recover the matter content, the equations of motion and Bianchi identities from group lattice and Cartan involution. Satake diagrams provide an elegant tool for the computations, the maximal oxidation dimension, and group disintegration chains can be directly read off. We give a complete list of theories that can be recovered from oxidation of a 3 dimensional coset sigma model on G/H, where G is…
We discuss fermionic reductions of type IIA superstrings on AdS4 x CP3 in relation to the conjectured AdS4/CFT3 duality. The superstring theory is described by means of a coset model construction, which is classically integrable. We discuss the global light-cone symmetries of the action and related kappa-symmetry gauge choices, and also present the complete quartic action in covariant form with respect to these. Further, we study integrable (fermionic) reductions, in particular, a reduction yielding a quadratic action of two complex fermions on the string world-sheet. Interestingly, this model…
Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two dimensions. These theories, the SU(N)/SO(N) and O(2P)/O(P) x O(P) models, are asymptotically free and exhibit charge fractionalization. When the instanton coupling theta=pi, they flow to the SU(N)_1 and O(2P)_1 conformal field theories, respectively. I also generalize the free energy computation to massive and massless perturbations of the coset conformal field theor…
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of freedom we construct the Pohlmeyer-reduced version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the origina…
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X_a and imply the one-loop scale invariance of the GS sigma model. In the special case when X_a is the gradient of a scalar ϕ(dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a…
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.
In this work the pure spinor formulation of the superstring is used to study quantum corrections to the left current OPE algebra of the coset $PSU(2, 2|4)/SO(4, 1) \times SO(5)$ sigma model, which describes the superstring dynamics in the $AdS_5 \times S^5$ background. In particular, the one loop corrections to the simple poles of the bosonic currents are computed. Unlike the case of the double poles, we show that the simple poles suffer corrections, which are important since the simple poles contribute to the four point amplitudes. We show that the only contribution to the simple poles comes …
We study dynamics of scalar fields on a large class of geometries described by integrable sigma models. Although equations of motion are not separable due to absence of isometries and Killing tensors, we completely determine the spectra using algebraic and group-theoretic methods.
We provide a new construction of the dressing cosets sigma-models which is based on an isotropic gauging of the E-models. As an application of this new approach, we show that the recently constructed multi-parametric integrable deformations of the principal chiral model are the dressing cosets, they are therefore automatically renormalizable and their dynamics can be completely characterized in terms of current algebras.
We show that a four-parameter generating solution for a general class of four-dimensional, spherically-symmetric, static, dyonic BPS saturated solutions of leading-order effective equations of toroidally compactified heterotic or type II superstring theory are exact string solutions. The corresponding ten-dimensional background defines a conformal sigma-model which is a particular case of a `chiral null model' with curved `transverse' part. The exact conformal invariance is a consequence of the chiral null structure of the `electric' part of the model and the N=4 world-sheet supersymmetry of i…
This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme, we present a number of interesting examples, including symmetric superspaces $G/G^{\mathbb{Z}_2}$ and coset superspaces…
Extended supersymmetric sigma-model is given, standing on the SO(2N+1) Lie algebra of fermion operators composed of annihilation-creation operators and pair operators. Canonical transformation, the extension of the SO(2N) Bogoliubov transformation to the SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we investigate a new aspect of the supersymmetric sigma-model on the Kaehler manifold of the symmetric space SO(2N+2)/U(N+1). We construct a Killing potential which is just the extension of the Killing potential in the …
The D=10 pure spinor constraint can be solved in terms of spinor moving frame variables and 8-component complex null vector which can be related to the kappa-symmetry ghost. Using this and similar solutions for the conjugate pure spinor and other elements of the non-minimal pure spinor formalism we present a (hopefully useful) reformulation of the measure of the pure spinor path integral for superstring in terms of products of Cartan form corresponding to the coset of 10D Lorentz group and to the coset of complex orthogonal group SO(8,C). Our study suggests a possible complete reformulation of…
The superstring theory in the light-cone gauge admits various gauge symmetries. Therefore, we gauge the superstring sigma model in the light-cone gauge under the gauge group SU(4). Some properties of the gauged action and the corresponding current will be studied. Besides, two modified actions for the superstring will be obtained.
We discuss special perturbations of the gauged level $k$ WZNW model inspired by the $σ$-model perturbation of the nonunitary WZNW model. In the large $k$ limit there is a second conformal point in the vicinity of the ultarviolet fixed point. At the second critical point the conformal model has a rational Virasoro central charge which no longer corresponds to a coset construction. In spite of this fact the perturbative conformal model appears to be a unitary system as long as the underlying coset construction at the ultraviolet critical point is unitary.
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 current…
The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric $N=2$ superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant CFTs. As an application, the theories are used as subtheories in tensor products with $c=9$, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polyno…
Computation of superstring partition function for the non-linear sigma model on the product of a two-torus and its dual within the scope of the doubled formalism is presented. We verify that it reproduces the partition functions of the toroidally compactified type--IIA and type--IIB theories for appropriate choices of the GSO projection.
