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Register a new userIntegrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
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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.
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The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in arXiv:1303.5995.
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.
We compute the one-loop world-sheet correction to partition function of $AdS_5 times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S^2 at the two loop level. We find that S^2 x S^2 x S^2 background is metastable and the effective action favors a single large S^2 in comparison to the remaining S^2 x S^2 in the models with Myers term. On the other hand, we find that a large S^2 x S^2 in comparison to the remaining S^2 is favored in IIB matrix model itself. We further study the stability of fuzzy S^2 x S^2 background in detail in IIB matrix model with respect to the scale factors of each S^2 as well. In this case, we find unstable directions which lower the effective action away from the most symmetric fuzzy S^2 x S^2 background.
The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.
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