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Register a new userThe Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
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We study operator insertions into the $1/2$ BPS Wilson loop in ${cal N}=4$ SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.
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We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $mathcal{N}=4$ super Yang-Mills theory. The operators we consider are defect changing operators, which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to perturbatively compute the area corresponding to boundary contours which are deformations of the circle. Our perturbative expansion is carried to high orders compared with the wavy approximation and yields new analytic results. The regularized area is invariant under a one parameter family of continuous deformations of the boundary contour which are not related to the global symmetry of the problem. We show that this symmetry of the Wilson loops breaks at weak coupling at an a priori unexpected order in the perturbative expansion. We also study the corresponding Lax operator and algebraic curve for these solutions.
The finite remainder function for planar, color-ordered, maximally helicity violating scattering processes in N=4 super Yang-Mills theory possesses a non-vanishing multi-Regge limit that depends on the choice of a Mandelstam region. We analyze the combined multi-Regge collinear limit in all Mandelstam regions through an analytic continuation of the Wilson loop OPE. At leading order, the former is determined by the gluon excitation of the Gubser-Klebanov-Polyakov string. We illustrate the general procedure at the example of the heptagon remainder function at two loops. In this case, the continuation of the leading order terms in the Wilson loop OPE suffices to determine the two-loop multi-Regge heptagon functions in all Mandelstam regions from their symbols. The expressions we obtain are fully consistent with recent results by Del Duca et al.
We perform exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite t Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. In particular, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.
We consider $alpha$ corrections to the one-loop four-point correlator of the stress-tensor multiplet in $mathcal{N}=4$ super Yang-Mills at order $1/N^4$. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS$_5times$S$^5$. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop-amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in $alpha$ not considered before.
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