# One-loop corrections to the celestial chiral algebra from Koszul Duality

## TL;DR

This paper explores one-loop quantum corrections to the celestial chiral algebra in self-dual Yang-Mills theory, utilizing Koszul duality to reproduce quantum deformations and ensure algebraic consistency.

## Contribution

It introduces a novel application of Koszul duality to compute quantum deformations of the celestial chiral algebra in SDYM theory.

## Key findings

- Successfully reproduces one-loop quantum deformation of the celestial chiral algebra
- Demonstrates the role of a quartic axion field in maintaining associativity at the quantum level
- Provides a framework connecting twistor space formulations with quantum algebraic structures

## Abstract

We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.