Burns-space scattering amplitudes and defect-free chiral-algebra correlators

Let WZW$_4$ plus Mabuchi gravity be the bulk theory on Burns space, and let the large $N$ chiral algebra be the chiral algebra obtained from the compactification $\overline{\operatorname{SL}}_2(\mathbb{C})$, with no defects and uniquely defined correlators. Burns-space/chiral-algebra correspondence conjecture. At all orders in $1/N$, the scattering amplitudes of WZW$_4$ plus Mabuchi gravity on Burns space coincide with the uniquely defined correlators of the large $N$ chiral algebra with no defects. This consequence is derived in the paper from the loop-level equality of holographic correlators and the Penrose transform; its validity therefore remains contingent on that open conjecture.