The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling

We compute the one-loop correction to the probe D3-brane action in AdS5 x S5 expanded around the classical Drukker-Fiol solution ending on a circle at the boundary. It is given essentially by the logarithm of the one-loop partition function of an Abelian ${cal N}=4$ vector multiplet in AdS2 x S2 geometry. This one-loop correction is expected to describe the subleading 1/N term in the expectation value of circular Wilson loop in the totally symmetric rank k representation in SU(N) SYM theory at strong coupling. In the limit k << N when the circular Wilson loop expectation values for the symmetric representation and for the product of k fundamental representations are expected to match we find that this one-loop D3-brane correction agrees with the gauge theory result for the k-fundamental case.

Correlation function of circular Wilson loop with two local operators and conformal invariance

We consider the correlation function of a circular Wilson loop with two local scalar operators at generic 4-positions in planar N=4 supersymmetric gauge theory. We show that such correlator is fixed by conformal invariance up to a function of t Hooft coupling and two scalar combinations of the positions invariant under the conformal transformations preserving the circle. We compute this function at leading orders at weak and strong coupling for some simple choices of local BPS operators. We also check that correlators of an infinite line Wilson loop with local operators are the same as those for the circular loop.

Correlation function of null polygonal Wilson loops with local operators

We consider the correlator <W_n O(x)> of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio zeta. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling lambda. We compute F(zeta,lambda) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.

Semiclassical four-point functions in AdS_5 x S^5

We consider a semiclassical (large string tension ~ lambda^1/2) limit of 4-point correlator of two heavy vertex operators with large quantum numbers and two light operators. It can be written in a factorized form as a product of two 3-point functions, each given by the integrated light vertex operator on the classical string solution determined by the heavy operators. We check consistency of this factorization in the case of a correlator with two dilatons as light operators. We study in detail the example when all 4 operators are chiral primary scalars, two of which carry large charge J of order of string tension. In the large J limit this correlator is nearly extremal. Its semiclassical expression is, indeed, found to be consistent with the general protected form expected for an extremal correlator. We demonstrate explicitly that our semiclassical result matches the large J limit of the known free N=4 SYM correlator for 4 chiral primary operators with charges J,-J,2,-2; we also compare it with an existing supergravity expression. As an example of a 4-point function with two non-BPS heavy operators, we consider the case when the latter are representing folded spinning with large AdS spin and two light states being chiral primary scalars.

On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT

We consider the 2-point function of string vertex operators representing string state with large spin in AdS_5. We compute this correlator in the semiclassical approximation and show that it has the expected (on the basis of state-operator correspondence) form of the strong-coupling limit of the 2-point function of single trace minimal twist operators in gauge theory. The semiclassical solution representing the stationary point of the path integral with two vertex operator insertions is found to be related to the large spin limit of the folded spinning string solution by a euclidean continuation, transformation to Poincare coordinates and conformal map from cylinder to complex plane. The role of the source terms coming from the vertex operator insertions is to specify the parameters of the solution in terms of quantum numbers (dimension and spin) of the corresponding string state. Understanding further how similar semiclassical methods may work for 3-point functions may shed light on strong-coupling limit of the corresponding correlators in gauge theory as was recently suggested by Janik et al in arXiv:1002.4613.