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Résumé |
The analytic conformal bootstrap has produced a wealth of results for four-point functions, from a universal large-spin expansion to the Lorentzian inversion formula and dispersion relations. Extending these tools to higher points is hampered by the rapid growth in the number of cross-ratios. Defect CFTs offer a setting where this growth is much milder while new data become accessible: correlators with a conformal defect probe bulk-to-defect couplings and the defect spectrum on top of the bulk CFT data. In this talk I consider the simplest such "multipoint" object, the three-point function of two bulk operators and one defect operator, and study its crossing equation in the lightcone limit. Unlike the bulk two-point function, the bulk channel is not dominated by the identity, so the leading contribution already carries dynamical information about the theory. Reproducing the exchange of the leading-twist bulk operator in the defect channel requires two new twist-accumulating families of defect operators at large transverse spin: "double-twist" operators built from the external bulk and defect fields, and, perhaps surprisingly, "triple-twist" operators involving two copies of the defect field. I will show how crossing fixes their defect CFT data at large transverse spin in terms of bulk OPE data, with closed-form expressions in suitable limits. I will then specialize to N=4 SYM with a half-BPS Maldacena–Wilson line, where the leading twist comes from the stress-tensor multiplet and the results become remarkably simple. I will conclude by discussing ongoing work on dispersion relations for bulk-bulk-defect correlators, applied to the correlator of two 20' operators and the tilt operator at strong coupling, as a first step towards reconstructing the correction beyond the disconnected result. Based on arXiv:2602.23428 with L. Bianchi and A. Mattiello, and work in progress. |
