$D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories

TL;DR

This paper demonstrates that the free six-dimensional , (4,0) theory can be obtained as a 'square' of the , (2,0) theory using a convolutive product, providing new insights into chiral conformal gravity and gauge-gravity relations.

Contribution

It introduces a convolutive product approach to derive the , (4,0) theory from the , (2,0) theory, extending the gauge gravity paradigm.

Findings

The , (4,0) theory emerges as a 'square' of the , (2,0) theory.

The approach offers a new perspective on chiral conformal gravity.

It generalizes the 'gravity = gauge gauge' paradigm.

Abstract

Using a convolutive field theoretic product, it is shown here that the "square" of an Abelian $D=6$, $\mathcal{N}=(2,0)$ theory yields the free $D=6$, $\mathcal{N}=(4,0)$ theory constructed by Hull, together with its generalised (super)gauge transformations. This offers a new perspective on the $(4, 0)$ theory and chiral theories of conformal gravity more generally, while at the same time extending the domain of the "gravity = gauge $\times$ gauge" paradigm.