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Register a new userMore Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
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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.
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We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 times mathbb{C}textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS$_2$ Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution.
A recent, integrability-based conjecture in the framework of the Wilson loop OPE for N=4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. We attach computer-readable files with our results, as well as an algorithm implementation which may be readily used to generate higher-loop corrections. The feasibility of obtaining the explicit kinematical dependence of the first term in the OPE in principle at arbitrary loop order, offers promise for the suitability of this approach as a non-perturbative description of Wilson loops/scattering amplitudes.
Proceedings of the workshop Boundary and Defect Conformal Field Theory: Open Problems and Applications, Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.
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.
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.
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