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Register a new userClassical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
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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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We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the kappa-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalans constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.
We discuss some new simple closed bosonic string solutions in AdS_5 x S^5 that may be of interest in the context of AdS/CFT duality. In the first part of this work we consider solutions with two spins (S_1, S_2) in AdS_5. Starting from the flat-space solutions and using perturbation theory in the curvature of AdS_5 space, we construct leading terms in the small two-spin solution. We find corrections to the leading Regge term in the classical string energy and uncover a discontinuity in the spectrum for certain type of a solution. We then analyze the connection between small-spin and large-spin limits of string solutions in AdS_5. We show that the S_1 = S_2 solution in AdS_5 found in earlier papers admits both limits only in simplest cases of the folded and rigid circular strings. In the second part of the paper we construct a new class of chiral solutions in R_t x S^5 for which embedding coordinates of S^5 satisfy the linear Laplace equations. They generalize the previously studied rigid string solutions. We study in detail a simple nontrivial example.
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.
We investigate the structure of the quantum S-matrix for perturbative excitations of the Pohlmeyer reduced version of the AdS_5 x S^5 superstring following arXiv:0912.2958. The reduced theory is a fermionic extension of a gauged WZW model with an integrable potential. We use as an input the result of the one-loop perturbative scattering amplitude computation and an analogy with simpler reduced AdS_n x S^n theories with n=2,3. The n=2 theory is equivalent to the N=2 2-d supersymmetric sine-Gordon model for which the exact quantum S-matrix is known. In the n=3 case the one-loop perturbative S-matrix, improved by a contribution of a local counterterm, satisfies the group factorization property and the Yang-Baxter equation, and reveals the existence of a novel quantum-deformed 2-d supersymmetry which is not manifest in the action. The one-loop perturbative S-matrix of the reduced AdS_5 x S^5 theory has the group factorisation property but does not satisfy the Yang-Baxter equation suggesting some subtlety with the realisation of quantum integrability. As a possible resolution, we propose that the S-matrix of this theory may be identified with the quantum-deformed [psu(2|2)]^2 x R^2 symmetric R-matrix constructed in arXiv:1002.1097. We conjecture the exact all-order form of this S-matrix and discuss its possible relation to the perturbative S-matrix defined by the path integral. As in the AdS_3 x S^3 case the symmetry of the S-matrix may be interpreted as an extended quantum-deformed 2-d supersymmetry.
We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S^5 angular momentum J and the string tension lambda. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with lambda=lambda/J^2 fixed recovers the plane-wave Hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit lambdato infty, J fixed, the energy of short strings scales as sqrt[4]{lambda} while the energy of long strings scales as sqrt{lambda}. We further show that the gauge-fixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum perfectly agrees with the one obtained earlier for some specific cases.
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