Self-Dual Gauge Theory from the Top Down

TL;DR

This paper establishes dualities between non-supersymmetric self-dual gauge theories on certain backgrounds and a 2d chiral defect CFT, using twisted holography and celestial chiral algebra correspondence.

Contribution

It introduces a novel duality framework connecting self-dual gauge theories with 2d defect CFTs via twisted holography on Calabi-Yau five-folds.

Findings

Bijective correspondence between 2d defect CFT states and celestial chiral algebra states.

Matching of operator products with collinear splitting amplitudes up to one-loop.

Derivation of a closed formula for certain two-loop all + amplitudes in gauge theory.

Abstract

We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of $4d$ self-dual asymptotically flat backgrounds, and the large $N$ limit of an independently defined $2d$ chiral defect CFT. Our construction goes via twisted holography for the type I topological string on a Calabi-Yau five-fold which fibres over twistor space. In particular, we show that single-trace operators of the $2d$ defect CFT are in bijection with states of the celestial chiral algebra. We match the operator products of these states with the collinear splitting amplitudes of the self-dual gauge theory up to one-loop. Assigning vacuum expectations to central operators in the boundary theory computes bulk amplitudes on self-dual backgrounds. We are able to extract form factors from these amplitudes, which we use to give a simple closed formula for certain $n$-point two-loop all $+$ amplitudes in $\mathrm{SU}(K) \times \mathrm{SU}(R)$ gauge theory coupled to bifundamental massless fermions.