Consistent S^2 Pauli Reduction of Six-dimensional Chiral Gauged Einstein-Maxwell Supergravity

TL;DR

This paper demonstrates a fully consistent S^2 Pauli reduction of six-dimensional chiral gauged supergravity, enabling solutions to be lifted from four to six dimensions, and explores implications for the cosmological constant and brane models.

Contribution

It provides the first complete consistent reduction of 6D supergravity on S^2, linking 4D solutions to 6D origins and addressing the cosmological constant problem.

Findings

All 4D N=1 supergravity solutions can be lifted to 6D.

The model constrains gauge couplings if the KK scale is 10^{-3} eV.

A connection to 5D orbifold models with branes is proposed.

Abstract

Six-dimensional N=(1,0) Einstein-Maxwell gauged supergravity is known to admit a (Minkowski)_4\times S^2 vacuum solution with four-dimensional N=1 supersymmetry. The massless sector comprises a supergravity multiplet, an SU(2) Yang-Mills vector multiplet, and a scalar multiplet. In this paper it is shown that, remarkably, the six-dimensional theory admits a fully consistent dimensional reduction on the 2-sphere, implying that all solutions of the four-dimensional N=1 supergravity can be lifted back to solutions in six dimensions. This provides a striking realisation of the idea, first proposed by Pauli, of obtaining a theory that includes Yang-Mills fields by dimensional reduction on a coset space. We address the cosmological constant problem within this model, and find that if the Kaluza-Klein mass scale is taken to be 10^{-3} eV (as has recently been suggested) then four-dimensional gauge-coupling constants for bulk fields must be of the order of 10^{-31}. We also suggest a link between a modification of the model with 3-branes, and a five-dimensional model based on an S^1/Z_2 orbifold.