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In a previous paper we showed that the electromagnetic superenergy tensor,the Chevreton tensor, gives rise to a conserved current when there is ahypersurface orthogonal Killing vector present. In addition, the current isproportional to the Killing vector. The aim of this paper is to extend thisresult to the case when we have a two-parameter Abelian isometry group thatacts orthogonally transitive on non-null surfaces. It is shown that forfour-dimensional Einstein-Maxwell theory with a source-free electromagneticfield, the corresponding superenergy currents lie in the orbits of the groupand are conserved. A similar result is also shown to hold for the trace of theChevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordontheory for the superenergy of the scalar field. This links up well with thefact that the Bel tensor has these properties and the possibility ofconstructing conserved mixed currents between the gravitational field and thematter fields.

Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups