Semiclassical short strings in AdS_5 x S^5

We present results for the one-loop correction to the energy of a class of string solutions in AdS_5 x S^5 in the short string limit. The computation is based on the observation that, as for rigid spinning string elliptic solutions, the fluctuation operators can be put into the single-gap Lame' form. Our computation reveals a remarkable universality of the form of the energy of short semiclassical strings. This may help to understand better the structure of the strong coupling expansion of the anomalous dimensions of dual gauge theory operators.Comment: 12 pages, one pdf figure. Invited Talk at 'Nonlinear Physics. Theory and Experiment VI', Gallipoli (Italy) - June 23 - July 3, 201

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio

Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions

Motivated by the desire to relate Bethe ansatz equations for anomalous dimensions found on the gauge theory side of the AdS/CFT correspondence to superstring theory on AdS_5 x S5 we explore a connection between the asymptotic S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum field theory. The latter generalizes the standard ``non-relativistic'' Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic Heisenberg spin chain and should be related to a limit of superstring effective action. We find the exact form of the quartic interaction terms in the generalized LL type action whose quantum S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders in the `t Hooft coupling an earlier computation of Klose and Zarembo of the S-matrix of the standard LL model. We also consider a generalization to the case when the spin chain S-matrix contains an extra ``string'' phase and determine the exact form of the LL 4-vertex corresponding to the low-energy limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the relation between the resulting ``non-relativistic'' non-local action and the second-derivative string sigma model. We comment on modifications introduced by strong-coupling corrections to the AFS phase. We mostly discuss the SU(2) sector but also present generalizations to the SL(2) and SU(1|1) sectors, confirming universality of the dressing phase contribution by matching the low-energy limit of the AFS-type spin chain S-matrix with tree-level string-theory S-matrix.Comment: 52 pages, 4 figures, Imperial-TP-AT-6-2; v2: new sections 7.3 and 7.4 computing string tree-level S-matrix in SL(2) and SU(1|1) sectors, references adde

Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators

We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.Comment: 23 pages, 1 Figur

Strings on type IIB pp-wave backgrounds with interacting massive theories on the worldsheet

We consider superstring theories on pp-wave backgrounds which result in an integrable ${\cal N}=(2,2)$ supersymmetric Landau-Ginzburg theory on the worldsheet. We obtain exact eigenvalues of the light-cone gauge superstring hamiltonian in the massive and interacting world-sheet theory with superpotential $Z^3-Z$. We find the modes of the supergravity part of the string spectrum, and their space-time interpretation. Because the system is effectively at strong coupling on the worldsheet, these modes are not in one-to-one correspondence with the usual type IIB supergravity modes in the $p_{-} \to 0$ limit. However, the above correspondence holds in the $\alpha'\to 0$ limit.Comment: 20 pages, 1 figure; minor changes, comments adde

Pulsating Strings in Lunin-Maldacena Backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS_5xS^5. We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS_5xS^5 we find a contribution which depends on the deformation parameter.Comment: 16 pages, 2 figures, typos fixe

Double-helix Wilson loops: case of two angular momenta

Recently, Wilson loops with the shape of a double helix have played an important role in studying large spin operators in gauge theories. They correspond to a quark and an anti-quark moving in circles on an S3 (and therefore each of them describes a helix in RxS3). In this paper we consider the case where the particles have two angular momenta on the S3. The string solution corresponding to such Wilson loop can be found using the relation to the Neumann-Rosochatius system allowing the computation of the energy and angular momenta of the configuration. The particular case of only one angular momentum is also considered. It can be thought as an analytic continuation of the rotating strings which are dual to operators in the SL(2) sector of N=4 SYM.Comment: 30 pages, 2 figures, LaTeX. v2: Small corrections, reference adde

Coordinate Bethe Ansatz for the String S-Matrix

We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS5 x S5, compatible with centrally extended su(2|2) symmetry.Comment: 25 Pages, plain LaTeX, 4 Figures. Mostly added references, fixed typo

Integrability of the N=2 boundary sine-Gordon model

We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements, refs added, to appear in J. Phys. A: Math. Ge

Infinite spin limit of semiclassical string states

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.Comment: 38 pages, 3 figures; v2: comments on derivation of bound states of magnons from discrete Bethe equations added in section 4 and appendix C, references added, Imperial-TP-AT-6-4, HUTP-06/A002