Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring $σ$-models with a $\mathbb{Z}_4$ coset target space. By applying the Lie algebra expansion to the isometry algebra, we obtain different $σ$-models, where the number of dynamical fields can change. We reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS$_5 \times$S$^5$). We define a criterion for the algebra truncation such that the equations of motion of the expanded action of the new $σ$-model are equivalent to the vanishing curvature condition of the Lax connection obtained by expanding the Lax connection of the initial model.
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.
The purpose of this contribution is to initiate the study of integrable deformations for different superstring theory formalisms that manifest the property of (classical) integrability. In this paper we choose the hybrid formalism of the superstring in the background AdS_{2}xS^{2} and explore in detail the most immediate consequences of its lambda-deformation. The resulting action functional corresponds to the lambda-model of the matter part of the fairly more sophisticated pure spinor formalism, which is also known to be classical integrable. In particular, the deformation preserves the integ…
For type II supergravity backgrounds with superisometries the corresponding transformations and conserved currents for the superstring are constructed up to fourth order in $Θ$. It is then shown how, for certain backgrounds related to near horizon geometries of intersecting branes, the components of the superisometry current can be used to construct a Lax connection demonstrating the classical integrability of the string in these backgrounds. This includes examples of $AdS_2$ and $AdS_3$ backgrounds with a $D(2,1;α)$ isometry group which have not previously been studied from an integrability p…
We show that the three strings vertex coefficients in light--cone open string field theory satisfy the Hirota equations for the dispersionless Toda lattice hierarchy. We show that Hirota equations allow us to calculate the correlators of an associated quantum system where the Neumann coefficients represent the two--point functions. We consider next the three strings vertex coefficients of the light--cone string field theory on a maximally supersymmetric pp--wave background. Using the previous results we are able to show that these Neumann coefficients satisfy the Hirota equations for the full …
We derive the AdS${}_5\times$S${}^5$ Green-Schwarz superstring from four-dimensional Beltrami-Chern-Simons theory reduced on a manifold with singular boundary conditions. In this construction, the Lax connection and spectral parameter of the integrable superstring have a simple geometric origin in four dimensions as gauge connection and reduction coordinate. Kappa symmetry arises as a certain class of singular gauge transformations, while the worldsheet metric comes from complex-structure-changing Beltrami differentials. Our approach offers the possibility of investigating integrable holograph…
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmet…
We discuss a classical integrability in the type IIB string theory on the AdS_5 x S^5 background. By using the Roiban-Siegel formulation of the superstring on the AdS_5 x S^5, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case, and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability …
We consider the monodromy matrix for the pure spinor IIB superstring on $AdS_5\times S^5$ at leading order at strong coupling, in particular its variation under an infinitesimal and continuous deformation of the contour. Such variation is equivalent to the insertion of a local operator. Demanding the BRST-closure for such an operator rules out its existence, implying that the monodromy matrix remains contour-independent at the first order in perturbation theory. Furthermore we explicitly compute the field strength corresponding to the flat connections up to leading order and directly check tha…
We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target su…
In this paper we continue the investigation of aspects of integrability of the type IIA AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) superstrings. By constructing a one parameter family of flat connections we prove that the Green-Schwarz string is classically integrable, at least to quadratic order in fermions, without fixing the kappa-symmetry. We then compare the quantum dispersion relation, fixed by integrability up to an unknown interpolating function h(lambda), to explicit one-loop calculations on the string worldsheet. For AdS(3) x S(3) x S(3) x S(1) the spectrum contains heavy, …
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.
We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action into itself. On bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2,4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transfor…
We consider bosonic subsectors of the q-deformed AdS_5 x S^5 superstring action and study the classical integrable structure of anisotropic Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving limits. The subsectors are 1) deformed AdS_3 x S^1 and 2) R x deformed S^3. The cases 1) and 2) lead to a time-like warped SL(2) LLSM and a squashed S^3 LLSM, respectively. For each of them, we construct an infinite number of non-local conserved charges and show a quantum affine algebra at the classical level. Furthermore, a pp-wave like limit is applied for the case 1). The resulting syste…
Type II supergravity admits an AdS(3) x S(2) x S(2) x T(3) solution with fluxes depending on several free parameters. We determine the constraints on these parameters imposed by the requirement of (classical) integrability of the superstring sigma model. To do this we analyze the low-energy effective action for the spinning GKP string. The absence of particle production in the tree-level S-matrix of bosonic excitations is shown to imply the vanishing of two of the four parameters in the NSNS three-form flux. This reduces the supergravity background to either the one-parameter AdS(3) x S(2) x S…
We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its classical dynamics, 1) rational and 2) trigonometric descriptions. The former 1) is based on the SU(2)_L symmetry and the latter 2) comes from the broken SU(2)_R symmetry. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related one another through a non-local map.
We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold $G/H$ are known to be classically integrable. We investigate a possibility to extend an argument of absence of quantum anomalies in non l…
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…
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…
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 lambda deformation of the pure spinor formalism of the superstring in the $AdS_{5}\times S^{5}$ background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its parent theory. It is also shown that the effective action takes the standard form of the Berkovits-Howe action functional, allowing to calculate the deformed background supergeometry in a straightforward way. The background fields coincide with those of the lambda model of the Green-Schwarz formalism, hence satisfying the same set of supergravity equations of…
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 generi…
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.
We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R due to the deformation. According to this symmetry, there are two descriptions to describe the classical dynamics of the system, 1) the SL(2,R)_L description and 2) the enhanced U(1)_R description. In the former 1), we show that the Yangian symmetry is realized by improving the SL(2,R)_L Noether c…
This article reviews the application of integrability to the spectral problem of strings on AdS_5 x S^5 and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we apply these ideas to the AdS_5 x S^5 string and in later chapters discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N=4 supersymmetry Yang-Mills …
In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma model coupled to a self-interacting massless fermion, while the bosonic one defines a one-parameter deformation of the O(2N) sigma model. For N=2 the latter model is equivalent to the integrable deformation of the O(4) sigma model discovered by Wiegmann. At higher values of N we find that integrability is more sporadic and requires a fine-tuning of the paramet…
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 conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature relation. Some new integrable two-dimensional sigma models are then presented.
This is a write-up of lectures on integrable sigma-models, which covers the following topics: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and beta-function, (5) S-matrix bootstrap in the O(N) model, (6) Supersymmetric cosets and strings on AdS(d)xX.
The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N=3 other possible boundary conditions are considered briefly.
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.
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 several classes of $σ$-models (on groups and symmetric spaces, $η$-models, $λ$-models) with local couplings that may depend on the 2d coordinates, e.g. on time $τ$. We observe that (i) starting with a classically integrable 2d $σ$-model, (ii) formally promoting its couplings $h_α$ to functions $h_α(τ)$ of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that $h_α(τ)$ must solve the 1-loop RG equations of the original theory with $τ$ interpreted as RG time. This provides a novel example of an 'integrability - RG flow' connecti…
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 integrability preserving boundary conditions for Green-Schwarz sigma-models on semi-symmetric spaces. The boundary conditions are expressed as gluing conditions of the flat-connection, using an involutive metric preserving automorphism. We show that the boundary conditions preserve half of the space-time supersymmetry and an infinite set of conserved charges. We find integrable D-brane configurations for AdS_5 x S^5 and AdS_4 x CP^3 backgrounds.
This review is devoted to the classical integrability of the AdS5xS5 superstring theory. It starts with a reminder of the corresponding action as a coset model. The symmetries of this action are then reviewed. The classical integrability is then considered from the lagrangian and hamiltonian points of view. The second part of this review deals with the gauge fixing of this theory. Finally, some aspects of the pure spinor formulation are also briefly reviewed.
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…
Recently, a gauged linear sigma model was proposed by Berkovits and Vafa which can be used to describe the AdS_5xS^5 superstring at finite and zero radius. In this paper we show that the model is classically integrable by constructing its first non-local conserved charge and a superspace Lax "quartet". Quantum conservation of the non-local charge follows easily from superspace rules.
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 …
Exact massive S-matrices for two dimensional sigma models on symmetric spaces SU(2N)/Sp(N) and Sp(2P)/Sp(P)*Sp(P) are conjectured. They are checked by comparison of perturbative and non perturbative TBA calculations of free energy in a strong external field. We find the mass spectrum of the models and calculate their exact mass gap.
We construct recursively an infinite number of Poisson structures for the supersymmetric integrable hierarchy governing the Pohlmeyer reduction of superstring sigma models on the target spaces AdS_{n}\times S^n, n=2,3,5. These Poisson structures are all non-local and not relativistic except one, which is the canonical Poisson structure of the semi-symmetric space sine-Gordon model (SSSSG). We verify that the superposition of the first three Poisson structures corresponds to the canonical Poisson structure of the reduced sigma model. Using the recursion relations we construct commuting charges …
The AdS/CFT correspondence provides a rich testing ground for many important topics in theoretical physics. The earliest and most striking example of the correspondence is the conjectured duality between the energy spectrum of type IIB superstring theory on AdS_5 x S^5 and the operator anomalous dimensions of N=4 supersymmetric Yang-Mills theory in four dimensions. While there is a substantial amount of evidence in support of this conjecture, direct tests have been elusive. The difficulty of quantizing superstring theory in a curved Ramond-Ramond background is compounded by the problem of comp…
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…
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.
Non-local conserved charges in two-dimensional sigma models with target spaces $SO(2n)/SO(n){\times}SO(n)$ and $Sp(2n)/Sp(n){\times}Sp(n)$ are shown to survive quantization, unspoiled by anomalies; these theories are therefore integrable at the quantum level. Local, higher-spin, conserved charges are also shown to survive quantization in the $SO(2n)/SO(n){\times}SO(n)$ models.
We perform a detailed test of the quantum integrability of the AdS_5 x S^5 superstring in uniform light-cone gauge in its near plane-wave limit. For this we establish the form of the general nested light-cone Bethe equations for the quantum string from the long range psu(2,2|4) Bethe equations of Beisert and Staudacher. Moreover the scheme for translating excited string states into Bethe root excitations is given. We then confront the direct perturbative diagonalization of the light-cone string Hamiltonian in the near plane-wave limit with the energy spectrum obtained from the general nested l…
We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the $S-$matrix of this QFT tends to the scattering matrix of the $O(N)$ sigma model. The perturbation theory, Bethe anzatz …
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…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda mo…
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.
This thesis is mainly devoted to studying integrable deformations of the ${\rm AdS}_5 \times {\rm S}^5$ superstring and generalized supergravity. We start to give a brief review of the ${\rm AdS}_5 \times {\rm S}^5$ superstring formulated in the Green-Schwartz formalism, and then introduce homogeneous Yang-Baxter (YB) deformation of the ${\rm AdS}_5 \times {\rm S}^5$ superstring based on $r$-matrices which are solutions to the homogeneous classical YB equation. By performing a supercoset construction, we derive the general formula for homogeneous YB deformed backgrounds associated with bosonic…
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.
We briefly review the covariant formulation of the Green-Schwarz superstring by Berkovits, and describe how a detailed tree-level and one-loop analysis of this model leads, for the first time, to a derivation of the low-energy effective action of the heterotic superstring while keeping target-space supersymmetry manifest. The resulting low-energy theory is old-minimal supergravity coupled to tensor multiplet. The dilaton is part of the compensator multiplet.
