The paper obtains a closed-form expression for the constrained Hodge dual of a p-form under the spherical constraint x_i x_i = 1, which reduces to the standard hypersurface Hodge star with unit normal.
Consistent S^2 Pauli Reduction of Six-dimensional Chiral Gauged Einstein-Maxwell Supergravity
1 Pith paper cite this work. Polarity classification is still indexing.
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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.
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Hodge Duals in Spherical Compactifications
The paper obtains a closed-form expression for the constrained Hodge dual of a p-form under the spherical constraint x_i x_i = 1, which reduces to the standard hypersurface Hodge star with unit normal.