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 quaternionic spaces that are obtained via c-map from the special Kählerian moduli spaces of Calabi-Yau threefolds.

U-invariants, black-hole entropy and fixed scalars

“…It turns out that these transformations are certain Cartan elements in K = G/H [27], that is they belong to O(1, 1) p ∈ K, with p = 1 for N = 5, p = 3 for N = 6, 8.…”

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

“…maximally non compact, forms of the corresponding U -duality groups, as it is the case for E 7(7) ). The maximal degree of the polynomial in the Iwasawa decomposition of E 7 (7) SU ( 8) in the 56 of E 7(7) is d = 27. On the other hand, the Iwasawa parametrization of axionic generators of E 7(7) , performed in [44], considers the maximal triangular subgroup of E 7 (7) , containing the D = 5 U -duality group G 5 ≡ G 5,Os = E 6(6) :…”

“…Such non compact forms of the Lie groups are relevant for supergravity [1,2,3,4,5,6,7,8]. Here the scalar sector of the theory is described by a non linear sigma model based on a non compact symmetric space with negative curvature G/K, where G is non compact and K is its maximal compact subgroup.…”

“…U Sp (8) (J Os 3 , q = 8) SO(As) . G 5,As occur in the second row of the symmetric Magic Square L 3 (A s , B s ) [68,65], whereas G 6,As occur in the first row of Table 10.…”

Non-supersymmetric Attractors in Symmetric Coset Spaces

“…In 2005, Sen showed that all extremal black holes, both supersymmetric and non-supersymmetric (non-BPS), exhibit attractor behavior [2]: it is a result of the near-horizon geometry of extremal black holes, rather than supersymmetry. Since then, non-BPS attractors have been a very active field of research (see for instance [3,4,5,6,7,8,9,10,11,12,13,14,15]). In particular, a microstate counting for certain non-BPS black holes was proposed in [16].…”