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Register a new userSemiclassical correlators of three states with large S^5 charges in string theory in AdS_5 x S^5
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We consider semiclassical computation of 3-point correlation functions of (BPS or non-BPS) string states represented by vertex operators carrying large charges in S5. We argue that the AdS5 part of the construction of relevant semiclassical solution involves the two basic ingredients: (i) configuration of three glued geodesics in AdS2 suggested by Klose and McLoughlin in arXiv:1106.0495 and (ii) a particular Schwarz-Christoffel map of the 3-geodesic solution in cylindrical (tau, sigma) domain into the complex plane with three marked points. This map is constructed using the expression for the AdS2 string stress tensor which is uniquely determined by the 3 scaling dimensions as noted by Janik and Wereszczynski in arXiv:1109.6262 (our solution, however, is different from theirs). We also find the S5 part of the solution and thus the full expression for the semiclassical part of the 3-point correlator for several examples: extremal and non-extremal correlators of BPS states and a particular correlator of small circular spinning strings in S3 part of S5. We demonstrate that for the BPS correlators the results agree with the large charge limit of the corresponding supergravity and free gauge theory expressions.
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We consider a semiclassical (large string tension ~ lambda^1/2) limit of 4-point correlator of two heavy vertex operators with large quantum numbers and two light operators. It can be written in a factorized form as a product of two 3-point functions, each given by the integrated light vertex operator on the classical string solution determined by the heavy operators. We check consistency of this factorization in the case of a correlator with two dilatons as light operators. We study in detail the example when all 4 operators are chiral primary scalars, two of which carry large charge J of order of string tension. In the large J limit this correlator is nearly extremal. Its semiclassical expression is, indeed, found to be consistent with the general protected form expected for an extremal correlator. We demonstrate explicitly that our semiclassical result matches the large J limit of the known free N=4 SYM correlator for 4 chiral primary operators with charges J,-J,2,-2; we also compare it with an existing supergravity expression. As an example of a 4-point function with two non-BPS heavy operators, we consider the case when the latter are representing folded spinning with large AdS spin and two light states being chiral primary scalars.
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 study non-planar correlators in ${cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.
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.
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