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 [1]. Analyticity of the formula in s implies that the scaling dimensions of the defect operators are aligned in Regge trajectories ∆(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 [2].

The functional bootstrap for boundary CFT

“…This is also very similar to what happens in the 1D bootstrap case, with our Dirichlet and Neumann cases being analogous to the fermionic and bosonic basis[20] 9. Our definition of N is such that it is a monoid with the ordinary addition operation.…”

“…for all n ∈ N. 9 The functional bootstrap equations are a set of fully non-perturbative constraints on the OPE and BOE data. Unlike the toy basis, the α, β, θ basis now provide an ideal starting point for a perturbative expansion around the generalized free solution.…”

“…In that work, unitarity and crossing symmetry was used to derive numerical bounds for general BCFTs, as well as exact results for the Wilson-Fisher fixed points in the presence of a boundary. Since then, many other works have studied and generalized this to conformal defects in a number of situations [7][8][9][10][11][12][13][14].…”

A study of quantum field theories in AdS at finite coupling

“…6 There have been remarkable development in the large spin expansion in the last few years. See for instance [24][25][26][27][28][29] for other important developments.…”

Bootstrapping the 3d Ising model at finite temperature

“…Our rough strategy is to truncate the thermal crossing equation and approximate it by a finite set of linear equations for a finite set of variables. In spirit, this is similar to the "severe truncation" method initiated by Gliozzi [18,19] and applied with some success in the boundary/defect bootstrap [20][21][22][23][24][25][26][27].…”