Universality at large transverse spin in defect CFT

Abstract

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large $s$, $s$ being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function. Analyticity of the formula in $s$ implies that the scaling dimensions of the defect operators are aligned in Regge trajectories $\hat{\Delta }(s)$. These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large $s$ spectrum in the spirit of the work of Alday and Maldacena.

45 pages, 6 figures, a few comments added to improve clarity of the exposition

References in corpus (23)

• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Comments on operators with large spin
• A spacetime derivation of the Lorentzian OPE inversion formula
• Gravitational S-matrix from CFT dispersion relations
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• A tauberian theorem for the conformal bootstrap
• Wilson Loops in N=4 SYM and Fermion Droplets
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Entanglement entropy across a deformed sphere
• Conformal Bootstrap At Large Charge
• TASI lectures on AdS/CFT
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Twist operators in higher dimensions
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Towards the exact Bremsstrahlung function of ABJM theory
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Hovering Black Holes from Charged Defects
• Operator product expansion for conformal defects
• Anomalous dimensions of spinning operators from conformal symmetry
• Double Trace Interfaces
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin

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