We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the maximal deformation limit kappa -> infinity this model is T-dua
l to flipped double Wick rotation of the target space AdS_5 x S^5, i.e. dS_5 x H^5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, kappa -> i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS_5 x S^5 superstring model. We also study in some detail similar deformations of the AdS_3 x S^3 and AdS_2 x S^2 supercosets. The bosonic part of the deformed AdS_3 x S^3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS_2 x S^2 case the role of the Fateev model is played by the 2d sausage model. The kappa = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS_n x S^n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS_3 x S^3 with more than one parameter.
N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a
non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1,1) acts off shell, using the fact that N=4 Poincare supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the one-loop effective action. We then study how this anomaly is reflected in the supergravity S-matrix. Calculating one-loop N=4 supergravity scattering amplitudes (with and without additional matter multiplets) using color/kinematics duality and the double-copy construction we find that a particular U(1) symmetry which was present in the tree-level amplitudes is broken at the quantum level. This breaking manifests itself in the appearance of new one-loop N=4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in N>4 supergravities). We discuss the relation between these symmetry-violating amplitudes and the corresponding U(1) anomalous term in the one-loop supergravity effective action.
We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ sqr
t lambda ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic el^2 ln^n el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.
We consider the world surface in AdS_5 that ends on two intersecting null lines at the boundary. The corresponding string partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric
gauge theory and thus determines the cusp anomaly function f(lambda) of the gauge coupling. The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a_1=1) and in arXiv:0707.4254 (a_2=- 3 log 2). Here we find that the 2-loop coefficient is a_2 = - K where K is the Catalans constant. This is in agreement (expected on general grounds) with the previous results for f(lambda) as the coefficient of log(S) term in the energy of closed spinning string in AdS_5. The string theory value for a_2 is in agreement with the numerical result in hep-th/0611135 and the recent analytic result in arXiv:0708.3933 for the solution of the BES equation following from the asymptotic Bethe ansatz for the spectrum of the theory. We explicitly verify the cancellation of 2-loop 2d logarithmic divergences thus demonstrating the quantum consistency of the AdS_5 x S^5 superstring. We also discuss the structure of higher loop string corrections to the cusp anomaly giving a 2d QFT diagrammatic interpretation to the strong-coupling expansion of the cusp anomaly function as solution of the BES equation found in arXiv:0708.3933.
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 t
erm 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.
An important ``observable of planar N=4 SYM theory is the scaling function f(lambda) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of light-like Wilson loops. The non-trivial relation between the
anomalous dimension and the Wilson interpretations of f(lambda) is well-understood on the perturbative gauge theory side of the AdS/CFT duality. In the first part of this paper we present the dual string-theory counterpart of this relation, to all orders in lambda^(-1/2) expansion. As a check, we explicitly compute the leading 1-loop string sigma model correction to the cusp Wilson loop, reproducing the same subleading coefficient in f(lambda) as found earlier in the spinning closed string case. The same function f(lambda) appears also in the resummed form of the 4-gluon amplitude as discussed at weak coupling by Bern, Dixon and Smirnov and recently found at the leading order at strong coupling by Alday and Maldacena (AM). Here we attempt to extend this approach to subleading order in lambda^(-1/2) by computing the IR singular part of 1-loop string correction to the corresponding T-dual Wilson loop. We discuss explicitly the 1-cusp case and comment on apparent problems with the dimensional regularization proposal of AM when directly applied order by order in strong coupling (inverse string tension) expansion.
We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed di
rectly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to zeta(3).
