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Register a new userOn integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
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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 identification of the parameters of the two models. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. For the AdS_2 x S^2 case we then explore the effect of this limit on the supergravity background associated to the lambda-deformed model. We also suggest that the two models may form a dual Poisson-Lie pair and provide direct evidence for this in the case of the integrable deformations of the coset associated with S^2.
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We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the maximal deformation limit kappa -> infinity this model is T-dual to flipped double Wick rotation of the target space AdS_5 x S^5, i.e. dS_5 x H^5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, kappa -> i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS_5 x S^5 superstring model. We also study in some detail similar deformations of the AdS_3 x S^3 and AdS_2 x S^2 supercosets. The bosonic part of the deformed AdS_3 x S^3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS_2 x S^2 case the role of the Fateev model is played by the 2d sausage model. The kappa = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS_n x S^n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS_3 x S^3 with more than one parameter.
We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1)^2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS_2 x S^2 x T^6. The S-matrix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.
Following recent work on GLSM localization, we work out curvature couplings for rigidly supersymmetric nonlinear sigma models with superpotential for general target spaces, describing both ordinary and twisted chiral superfields on round two-sphere worldsheets. We briefly discuss why, unlike four-dimensional theories, there are no constraints on Kahler forms in these theories. We also briefly discuss general issues in topological twists of such theories.
We develop the 1/N expansion for stable string bit models, focusing on a model with bit creation operators carrying only transverse spinor indices a=1,...,s. At leading order (1/N=0), this model produces a (discretized) lightcone string with a transverse space of $s$ Grassmann worldsheet fields. Higher orders in the 1/N expansion are shown to be determined by the overlap of a single large closed chain (discretized string) with two smaller closed chains. In the models studied here, the overlap is not accompanied with operator insertions at the break/join point. Then the requirement that the discretized overlap have a smooth continuum limit leads to the critical Grassmann dimension of s=24. This protostring, a Grassmann analog of the bosonic string, is unusual, because it has no large transverse dimensions. It is a string moving in one space dimension and there are neither tachyons nor massless particles. The protostring, derived from our pure spinor string bit model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8 compactified bosonic dimensions, leaving 8 Grassmann dimensions--the worldsheet content of the superstring. If the transverse space of the protostring could be decompactified, string bit models might provide an appealing and solid foundation for superstring theory.
In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the $rm AdS_3 times S^3 times M^4$ string sigma model.
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