Lightcone Bootstrap for Multipoint Defect Correlators

Abstract

We initiate the lightcone bootstrap analysis of multipoint correlators in a defect conformal field theory. The setup we consider is the three-point function of two bulk and one defect operator. Requiring consistency of the crossing equation in the lightcone limit, we find constraints on the defect spectrum at large transverse spin. Specifically, to reproduce the exchange of the leading-twist operator in the bulk channel we find two new twist-accumulating families of defect operators at large transverse spin and we compute their defect CFT data in this limit.

Figures (6)

• Figure 1: Examples of multipoint defect correlators with their respective number of conformal cross-ratios.
• Figure 2: A schematic representation of the crossing equation for the bulk-bulk-defect correlator. The red curly line indicates the $\bar{z}\to 1$ lightcone limit we are considering, where the two bulk operators become lightlike separated. The defect operator $\hat{\phi}$ acts as a spectator in both OPE channel decompositions.
• Figure 3: The role of the $z,\bar{z}$ cross ratios can be easily understood in the conformal frame where the two bulk operators lie on a Minkowski plane orthogonal to the defect $\mathcal{D}$. The $z=0$ and $\bar{z}=0$ lines represent the defect lightcone, while the $z=1$ and $\bar{z}=1$ lines correspond to the two bulk operators being lightlike separated.
• Figure 4: A schematic representation of the crossing equation for the bulk two-point function. The red curly line indicates the $\bar{z}\to 1$ lightcone limit we are considering, where the two bulk operators become lightlike separated.
• Figure 5: The role of the $z,\bar{z}$ cross ratios is the same as for the case of the bulk two-point function. The two bulk operators lie on a Minkowski plane orthogonal to the defect $\mathcal{D}$. The defect operator $\hat{\phi}$ is located along the defect at a distance $x$ from the transverse plane.