R-R scalars, U-duality and solvable Lie algebras

Abstract

We consider the group theoretical properties of R-R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra G s ⊂ U of the U-duality algebra that generates the scalar manifold of the theory: exp[ G s] = U/H . Peccei-Quinn symmetries are naturally related with the maximal abelian ideal A ⊂ G s of the solvable Lie algebra. The solvable algebras of maximal rank occurring in maximal supergravities in diverse dimensions are described in some detail. A particular example of a solvable Lie algebra is a rank one, 2( h 2,1+2)-dimensional algebra displayed by the classical quatemionic spaces that are obtained via the c-map from the special Kählerian moduli spaces of Calabi-Yau threefolds.