Universality at large transverse spin in defect CFT

Understand

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 $\widehat{\Delta}(s)$.