Consistent S² Pauli Reduction of Six-dimensional Chiral Gauged Einstein-Maxwell Supergravity

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Six-dimensional N=(1,0) Einstein-Maxwell gauged supergravity is known to admit a (Minkowski)₄× S² 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 S¹/Z₂ orbifold.