Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5

We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the leading one-loop corrections to the dispersion relations of the excitations near a long spinning string in AdS. This investigation is partially motivated by the OPE-based approach to the computation of the expectation value of null polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial agreement with the recent asymptotic Bethe ansatz computation in arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in the ABA approach) is stable and has a corrected one-loop dispersion relation similar to the other massive modes. Its stability might hold also at the next-to-leading order as we suggest using a unitarity-based argument.Comment: 22 pages, 3 figures. v3: small corrections and a comment added in sec. 4.

Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring

We revisit the computation of the 2-loop correction to the energy of a folded spinning string in AdS_5 with an angular momentum J in S^5 in the scaling limit log S, J >>1 with J / log S fixed. This correction gives the third term in the strong-coupling expansion of the generalized scaling function. The computation, using the AdS light-cone gauge approach developed in our previous paper, is done by expanding the AdS_5 x S^5 superstring partition function near the generalized null cusp world surface associated to the spinning string solution. The result corrects and extends the previous conformal gauge result of arXiv:0712.2479 and is found to be in complete agreement with the corresponding terms in the generalized scaling function as obtained from the asymptotic Bethe ansatz in arXiv:0805.4615 (and also partially from the quantum O(6) model and the Bethe ansatz data in arXiv:0809.4952). This provides a highly nontrivial strong coupling comparison of the Bethe ansatz proposal with the quantum AdS_5 x S^5 superstring theory, which goes beyond the leading semiclassical term effectively controlled by the underlying algebraic curve. The 2-loop computation we perform involves all the structures in the AdS light-cone gauge superstring action of hep-th/0009171 and thus tests its ultraviolet finiteness and, through the agreement with the Bethe ansatz, its quantum integrability. We do most of the computations for a generalized spinning string solution or the corresponding null cusp surface that involves both the orbital momentum and the winding in a large circle of S^5.Comment: 50 pages, late

On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group

We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At the planar level, the difference to the case of gauge group SU(N) is only due to certain states being projected out, however at the non-planar level novel effects appear: While 1/N-corrections in the SU(N) case are always associated with splitting and joining of spin chains, this is not so for SO(N) and Sp(N). Here the leading 1/N-corrections, which are due to non-orientable Feynman diagrams in the field theory, originate from a term in the dilatation operator which acts inside a single spin chain. This makes it possible to test for integrability of the leading 1/N-corrections by standard (Bethe ansatz) means and we carry out various such tests. For orthogonal and symplectic gauge group the dual string theory lives on the orientifold AdS5xRP5. We discuss various issues related to semi-classical strings on this background.Comment: 25 pages, 3 figures. v2: Minor clarifications, section 5 expande

Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge

We consider the AdS_5 x S^5 superstring in the light-cone gauge adapted to a massless geodesic in AdS5 in the Poincare patch. The resulting action has a relatively simple structure which makes it a natural starting point for various perturbative quantum computations. We illustrate the utility of this AdS light-cone gauge action by computing the 1-loop and 2-loop corrections to the null cusp anomalous dimension reproducing in a much simpler and efficient way earlier results obtained in conformal gauge. This leads to a further insight into the structure of the superstring partition function in non-trivial background.Comment: 21pages, Late

New Penrose Limits and AdS/CFT

We find a new Penrose limit of AdS_5 x S^5 giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the SU(2) sector of N=4 SYM, this new Penrose limit is instead useful for studying the SU(2|3) and SU(1,2|3) sectors. In addition to the new Penrose limit of AdS_5 x S^5 we also find a new Penrose limit of AdS_4 x CP^3.Comment: 30 page

Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match

We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.Comment: 36 pages. v2: figure added, references adde

Quantum folded string and integrability: from finite size effects to Konishi dimension

Using the algebraic curve approach we one-loop quantize the folded string solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit result valid for arbitrary values of its Lorentz spin S and R-charge J in terms of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and derive the leading three coefficients of strong coupling expansion of short operators. Notably, our result evaluated for the anomalous dimension of the Konishi state gives 2\lambda^{1/4}-4+2/\lambda^{1/4}. This reproduces correctly the values predicted numerically in arXiv:0906.4240. Furthermore we compare our result using some new numerical data from the Y-system for another similar state. We also revisited some of the large S computations using our methods. In particular, we derive finite--size corrections to the anomalous dimension of operators with small J in this limit.Comment: 20 pages, 1 figure; v2: references added, typos corrected; v3: major improvement of the references; v4: Discussion of short operators is restricted to the case n=1. This restriction does not affect the main results of the pape

From Polygon Wilson Loops to Spin Chains and Back

Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator Product Expansion in terms of a transition amplitude on top of a color flux tube (FT). That picture is valid at any value of the 't Hooft coupling. So far it has been efficiently used at weak coupling (WC) in cases where only a single particle is flowing. At any finite value of the coupling however, an infinite number of particles are flowing on top of the color FT. A major open problem in this approach was how to deal with generic multi-particle states at WC. In this paper we study the propagation of any number of FT excitations at WC. We do this by first mapping the WL into a sum of two point functions of local operators. This map allows us to translate the integrability techniques developed for the spectrum problem back to the WL. E.g., the FT Hamiltonian can be represented as a simple kernel acting on the loop. Having an explicit representation for the FT Hamiltonian allows us to treat any number of particles on an equal footing. We use it to bootstrap some simple cases where two particles are flowing, dual to N2MHV amplitudes. The FT is integrable and therefore has other (infinite set of) conserved charges. The generating function of conserved charges is constructed from the monodromy (M) matrix between sides of the polygon. We compute it for some simple examples at leading order at WC. At strong coupling (SC), these Ms were the main ingredients of the Y-system solution. To connect the WC and SC computations, we study a case where an infinite number of particles are propagating already at leading order at WC. We obtain a precise match between the WC and SC Ms. That match is the WL analogue of the well known Frolov-Tseytlin limit where the WC and SC descriptions become identical. Hopefully, putting the WC and SC descriptions on the same footing is the first step in understanding the all loop structure.Comment: 52 pages, 14 figures, the abstract in the pdf is not encrypted and is slightly more detaile