R--R Scalars, U--Duality and Solvable Lie Algebras

Details R--R Scalars, U--Duality and Solvable Lie Algebras R--R Scalars, U--Duality and Solvable Lie Algebras

1996-11-04

arxiv.org/abs/hep-th/9611014v3

Nucl.Phys. B496 (1997) 617-629

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, misprints in Table 2 corrected

Scientific paper

10.1016/S0550-3213(97)00220-4

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 $\IG_s\subset U$ of the U--duality algebra that generates the scalar manifold of the theory: $\exp[\IG_s]= U/H$. Peccei-Quinn symmetries are naturally related with the maximal abelian ideal ${\cal A} \subset \IG_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 quaternionic spaces that are obtained via c-map from the special K\"ahlerian moduli spaces of Calabi-Yau threefolds.

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