Toward null-state equations in d > 2

Abstract

Abstract In two-dimensional CFTs with a large central charge, the level-two BPZ equation governs the heavy-light scalar four-point correlator when the light probe scalar has dimension h = $$ -\frac{1}{2} $$ − 1 2 ; the corresponding linear ordinary differential equation can be recast into a schematic form x2uxx + u = 0. In this paper, we make an observation that in a class of four-dimensional CFTs with a large central charge, the heavy-light scalar correlator in the near-lightcone limit obeys a similar equation, x3uxxxy + u = 0, when the light scalar has dimension ∆ = –1. We focus on the multi-stress tensor sector of the theory and also discuss the corresponding equations for the cases with ∆ = –2, –3. The solutions to these linear partial differential equations in higher dimensions are shown, after a suitable change of variables, to reproduce the near-lightcone correlators previously obtained via holography and the conformal bootstrap.