Actions for Biconformal Matter

TL;DR

This paper extends biconformal gauge theory to include scalar matter fields, showing that in a torsion-free setting, the Einstein and Klein-Gordon equations naturally emerge on an n-dimensional submanifold.

Contribution

It introduces scalar matter fields into biconformal gauge theory and demonstrates their influence on the geometric and physical equations in a torsion-free context.

Findings

The Einstein equation is recovered on an n-dimensional submanifold.

The scalar field satisfies the Klein-Gordon equation.

The stress-energy tensor acts as a source in the Einstein equation.

Abstract

We extend 2n-dim biconformal gauge theory by including Lorentz-scalar matter fields of arbitrary conformal weight. For a massless scalar field of conformal weight zero in a torsion-free biconformal geometry, the solution is determined by the Einstein equation on an n-dim submanifold, with the stress-energy tensor of the scalar field as source. The matter field satisfies the n-dim Klein-Gordon equation.