Burns space and holography

Abstract

We elaborate on various aspects of our top-down celestial holographic duality wherein the semiclassical bulk spacetime is a 4d asymptotically flat, self-dual K\"ahler geometry known as Burns space. The bulk theory includes an open string sector comprising a 4d WZW model and a closed string sector called "Mabuchi gravity" capturing fluctuations of the K\"ahler potential. Starting with the type I topological B-model on the twistor space of flat space, we obtain the twistor space of Burns space from the backreaction of a stack of $N$ coincident D1 branes, while the chiral algebra is obtained from (a twist of) the brane worldvolume theory. One striking consequence of this duality is that all loop-level scattering amplitudes of the theory on Burns space can be expressed as correlation functions of an explicit 2d chiral algebra. We also present additional large-$N$ checks, matching several 2 and 3-point amplitudes and their collinear expansions in the WZW$_4$ sector, and the mixed WZW$_4$-Mabuchi sector, of the bulk theory to the corresponding 2 and 3-point vacuum correlators and operator product expansions in the dual chiral algebra. Key features of the duality, along with our main results, are summarized in the introduction.