Top-down holography in an asymptotically flat spacetime

TL;DR

This work proposes a top-down holographic duality between a four-dimensional $SO(8)$ WZW$_4$ model on Burns space and a two-dimensional defect chiral algebra on $\mathbb{CP}^1$, framed within twisted holography and twistor uplift. The authors construct the bulk theory (WZW$_4$ coupled to scalar-flat Kähler gravity on Burns space) and its boundary dual (BRST-reduced symplectic-boson chiral algebra with $SO(8)$ flavor) and establish a dictionary identifying bulk soft modes $\phi_a[k,l](z)$ with boundary currents $J_a[k,l](z)$ in the planar limit. They perform concrete 2- and 3-point tests, deriving explicit two- and three-point bulk amplitudes on Burns space and matching them to OPE data of the boundary chiral algebra, including a current algebra at level $-2N$. The results provide a non-perturbative (finite-$N$) foothold for asymptotically flat holography via twisted string theory, illuminating how bulk collinear limits encode boundary operator product expansions and suggesting extensions to include gravitational sectors and self-dual gravity. The work connects celestial holography, twistor theory, and Beem-type chiral algebras in a concrete, calculable setting with explicit dictionary entries and nontrivial checks.

Abstract

We propose a holographic duality for a four dimensional WZW model with target manifold $\mathrm{SO}(8)$, coupled to scalar-flat Kähler 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.