The Spherically Symmetric Standard Model with Gravity

TL;DR

This paper revisits spherical reduction in four-dimensional theories, defining three notions of symmetry, and combines various formalisms to present a spherically reduced Standard Model with gravity as a two-dimensional dilaton gravity theory.

Contribution

It introduces a unified approach to spherical reduction across different sectors of the Standard Model coupled with gravity, utilizing multiple formalisms for clarity.

Findings

Different formalisms are optimal for different sectors.

The Standard Model with gravity can be reduced to a 2D dilaton gravity theory.

A comprehensive framework for spherical symmetry in particle physics and gravity.

Abstract

Spherical reduction of generic four-dimensional theories is revisited. Three different notions of "spherical symmetry" are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and scalar fields. In each sector a different formalism seems to be most convenient: the Cartan formulation of gravity works best in the purely gravitational sector, the Einstein formulation is convenient for the Yang-Mills sector and for reducing scalar fields, and the Newman-Penrose formalism seems to be the most transparent one in the fermionic sector. Combining them the spherically reduced Standard Model of particle physics together with the usually omitted gravity part can be presented as a two-dimensional (dilaton gravity) theory.