Twisted Holography and Celestial Holography from Boundary Chiral Algebra

TL;DR

This paper explores the dimensional reduction of 6d holomorphic theories to 3d, analyzing their boundary chiral algebras and connecting twisted and celestial holography through a unified algebraic framework.

Contribution

It introduces a BV formalism approach to KK reduction of 6d theories and relates boundary chiral algebras to holographic dualities via Koszul duality.

Findings

Effective interactions derived at all orders using homotopy transfer

Boundary chiral algebra matches universal defect algebra under certain conditions

Framework unifies twisted and celestial holography via boundary algebra analysis

Abstract

We study the Kaluza-Klein reduction of various $6d$ holomorphic theories. The KK reduction is analyzed in the BV formalism, resulting in theories that come from the holomorphic topological twist of $3d$ $\mathcal{N} = 2$ supersymmetric field theories. Effective interactions of the KK theories at the classical level can be obtained at all orders using homotopy transfer theorem. We also analyze a deformation of the theories that comes from deforming the spacetime geometry to $SL_2(\mathbb{C})$ due to the brane back-reaction. We study the boundary chiral algebras for the various KK theories. Using Koszul duality, we argue that by properly choosing a boundary condition, the boundary chiral algebra coincides with the universal defect chiral algebra of the original theory. This perspective provides a unified framework for accessing the chiral algebras that arise from both twisted holography and celestial holography programs.