10 = 6 + 4

TL;DR

This paper explores an alternative decomposition of higher-dimensional physics models, replacing the traditional 4+6 split with a 6+4 split involving conformal symmetry and complex projective space, offering new perspectives on internal symmetries.

Contribution

It proposes a novel 6+4 decomposition of higher-dimensional models using conformal symmetry and CP2, providing a different framework for understanding internal symmetries.

Findings

Introduces a 6-dimensional spacetime with conformal symmetry.

Identifies CP2 as a natural internal symmetry space.

Suggests alternative symmetry decompositions for higher-dimensional models.

Abstract

Some physics models have 10 dimensions that are usually decomposed into: 4 spacetime dimensions with local Lorentz Spin(1,3) symmetry plus a 6-dimensional compact space related to internal symmetries. A possibly useful alternative decomposition is into: 6 spacetime dimensions with local Conformal symmetry of the Conformal Group C(1,3) = Spin(2,4) = SU(2,2) plus a 4-dimensional compact Internal Symmetry Space that can be taken to be complex projective 2-space CP2 which, since CP2 = SU(3) / U(2), is a natural representation space for SU(3) and is a natural local representation space for U(2) = SU(2) x U(1).