Letter: Charging Symmetries and Linearizing Potentials for Gravity Models with Symplectic Symmetry

In this letter we continue to study a class offour-dimensional gravity models with n Abelian vectorfields and Sp(2n, R)/U(n) coset of scalar fields. Thisclass contains General Relativity (n = 0) andEinstein-Maxwell dilaton axion theory (n = 1),which arises in the low energy limit of heterotic stringtheory. We perform reduction of the model with arbitraryn to three dimensions and study the subgroupof non-gauge symmetries of the resultingtheory. First, we find an explicit form these symmetriesusing the Ernst matrix potential formulation. Second, weconstruct a new matrix variable which linearlytransforms under the action of the non-gaugetransformations. Finally, we establish one generalinvariant of the non gauge symmetry subgroup, whichallows us to clarify this subgroup structure.