Top-down holography in an asymptotically flat spacetime

We propose a holographic duality for a four dimensional WZW model with target manifold $\mathrm{SO}(8)$, coupled to scalar-flat K\"ahler gravity on an asymptotically flat, four dimensional background known as the Burns metric. The holographic dual is a two dimensional chiral algebra built out of gauged beta-gamma systems with $\mathrm{SO}(8)$ flavor. We test the duality by matching two-point correlators of soft gluon currents with two-point gluon amplitudes, and their leading OPE coefficients with collinear limits of three-point gluon amplitudes.