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We study string quantum corrections to the ratio of latitude and circular Wilson loops in N=4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS(5)xS(5) is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field-theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluating phaseshifts for all the fluctuation modes., Comment: 26 pages, 3 figures; v2: minor misprints corrected, no changes in the equations

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series., Comment: v2, published version

Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate fermionic Wess-Zumino term. We determine the full one-loop dilation operator of the theory. It involves an interesting new XXZ-like interaction term. Eigenvalues of our dilation operator, i.e. the one-loop anomalous dimensions, are computed for a few examples.

It has been observed more than 25 years ago that sigma model perturbation theory suffers from strongly RG-relevant high-gradient operators. The phenomenon was first seen in 1-loop calculations for the O(N) vector model and it is known to persist at least to two loops. More recently, Ryu et al. suggested that a certain deformation of the psl(N|N) WZNW-model at level k = 1, or equivalently the psl(N|N) Gross-Neveu model, could be free of RG-relevant high-gradient operators and they tested their suggestion to leading order in perturbation theory. In this note we establish the absence of strongly RG-relevant high-gradient operators in the psl(2|2) Gross-Neveu model to all loops. In addition, we determine the spectrum for a large subsector of the model at infinite coupling and observe that all scaling weights become half-integer. Evidence for a conjectured relation with the CP^1|2 sigma model is not found., Comment: 14 pages

Sigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence. In this work we apply recent general results on the spectrum of coset space models and on supergroup WZNW models to study the conformal sigma model with target space S^{3|2}. We construct its vertex operators and provide explicit formulas for their anomalous dimensions, at least to leading order in the sigma model coupling. The results are used to revisit a non-perturbative duality between the supersphere and the OSP(4|2) Gross-Neveu model that was conjectured by Candu and Saleur. With the help of powerful all-loop results for 1/2 BPS operators in the Gross-Neveu model we are able to recover the entire zero mode spectrum of the sigma model at a certain finite value of the Gross-Neveu coupling. In addition, we argue that the sigma model constraints and equations of motion are implemented correctly in the dual Gross-Neveu description. On the other hand, high(er) gradient operators of the sigma model are not all accounted for. It is possible that this discrepancy is related to an instability from high gradient operators that has previously been observed in the context of Anderson localization.

We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S(5). While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first vs second derivative kinetic terms, presence vs absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of sixteen fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra "massless" fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S(2) x T(6) by studying several particular examples of string solutions., Comment: 28 pages; v2: minor corrections, references updated

We construct topological Wess-Zumino term for supercoset sigma-models on various AdS(3) backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappa-symmetry and conformal invariance are equivalent to each other., Comment: 27 pages, 1 figure, v2: misprints corrected, reference added, v3: misprints in (4.1) and (4.2) corrected

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones., Comment: 28 pages; v2: References added

We study the string instanton wrapping a non-trivial two-cycle in CP(3) of the type IIA string theory compactified on AdS_4 x CP(3) superspace and find that it has twelve fermionic zero modes associated with 1/2 of the supersymmetry of the background thus manifesting that this classical instanton configuration is 1/2 BPS, Comment: 1+28 pages; v2: Section 3.1 extended, summary and discussion added; v3: added references, clarifications and Section 4.2 on supersymmetry properties of the instanton