Nonlocal Charges for Bonus Yangian Symmetries of Super-Yang-Mills

The existence of a "bonus" U(1) level-one Yangian symmetry of N=4 super-Yang-Mills has recently been proposed. We provide evidence for this proposal by constructing the BRST-invariant nonlocal charge in the pure spinor sigma model corresponding to this bonus level-one symmetry. We also construct analogous charges for bonus U(1) symmetries at all odd levels of the Yangian.Comment: LaTeX 16p

Quantum Current Algebra for the AdS5×S5AdS_5 \times S^5 Superstring

The sigma model describing the dynamics of the superstring in the $AdS_5 \times S^5$ background can be constructed using the coset $PSU(2,2|4)/SO(4,1)\times SO(5)$. A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE's is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE's. We also compute the OPE's of the left invariant currents with the energy momentum tensor at tree level and one loop.Comment: 28 pages, 12 figures, v2: typos corrected

First-principles derivation of the AdS/CFT Y-systems

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio

Exceptional Operators in N=4 super Yang-Mills

We consider one particularly interesting class of composite gauge-invariant operators in N=4 super Yang-Mills theory. An exceptional feature of these operators is that in the Thermodynamic Bethe Ansatz approach the one-loop rapidities of the constituent magnons are shown to be exact in the 't Hooft coupling constant. This is used to propose the mirror TBA description for these operators. The proposal is shown to pass several non-trivial checks.Comment: 40 pages, 2 figures, 1 attached Mathematica noteboo

Strings on Semisymmetric Superspaces

Several string backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. Their target space is always a Z(4) supercoset (a semi-symmetric superspace). Here we list all semi-symmetric cosets which have zero beta function and central charge c<=26 at one loop in perturbation theory.Comment: 25 pages, 1 figur

Numerical results for the exact spectrum of planar AdS4/CFT3

We compute the anomalous dimension for a short single-trace operator in planar ABJM theory at intermediate coupling. This is done by solving numerically the set of Thermodynamic Bethe Ansatz equations which are expected to describe the exact spectrum of the theory. We implement a truncation method which significantly reduces the number of integral equations to be solved and improves numerical efficiency. Results are obtained for a range of 't Hooft coupling lambda corresponding to $0 \leq h(\lambda) \leq 1$, where h(lambda) is the interpolating function of the AdS4/CFT3 Bethe equations.Comment: v3: corrected Acknowledgements section; v4: minor changes, published version; v5: fixed typos in Eq. (3.9

Integrable models: from dynamical solutions to string theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. Some integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the Bethe Ansatz solution of the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the seventieth anniversaries of Andr\'{e} Swieca (in memoriam) and Roland K\"{o}berle.Comment: 24 pages, to appear in Brazilian Journal of Physic

Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2 and D_2 on page 29 we corrected the rational part of the strong coupling predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table

Quasi-local formulation of the mirror TBA

We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are connected by the TBA equations are at most next to nearest neighbors with respect to the Y-system diagram of AdS/CFT.Comment: 13 pages, LaTe