Heavy States in 3d Gravity and 2d CFT

One way to learn about black holes and other heavy states in quantum gravity is to study their response to perturbations by light probe fields. In 3d gravity and holographic 2d CFTs, it is often possible to do this exactly. We consider the propagator of free scalar fields in AdS geometries with a conical defect or a BTZ black hole, dual on the boundary to a heavy-light 4-point function. In the bulk, the correlator can be computed by solving the equation of motion, as well as by the method of images. Below the BTZ threshold, both calculations have CFT interpretations in terms of the Virasoro blocks that enter the s-channel and t-channel OPEs. The corresponding OPE coefficients compute the amplitudes to create excitations of the scalar orbiting the defect, as well as the expectation values of light operators that form two-particle bound states of the scalar. We find that these expectation values remain finite near the BTZ threshold, where the scalar correlator exhibits a continuous phase transition.