192 research outputs found
The -map, Tits Satake subalgebras and the search for inflaton potentials
In this paper we address the general problem of including inflationary models
exhibiting Starobinsky-like potentials into (symmetric)
supergravities. This is done by gauging suitable abelian isometries of the
hypermultiplet sector and then truncating the resulting theory to a single
scalar field. By using the characteristic properties of the global symmetry
groups of the supergravities we are able to make a general
statement on the possible -attractor models which can obtained upon
truncation. We find that in symmetric models group theoretical
constraints restrict the allowed values of the parameter to be
. This confirms and generalizes results
recently obtained in the literature. Our analysis heavily relies on the
mathematical structure of symmetric supergravities, in
particular on the so called -map connection between Quaternionic K\"ahler
manifolds starting from Special K\"ahler ones. A general statement on the
possible consistent truncations of the gauged models, leading to
Starobinsky-like potentials, requires the essential help of Tits Satake
universality classes. The paper is mathematically self-contained and aims at
presenting the involved mathematical structures to a public not only of
physicists but also of mathematicians. To this end the main mathematical
structures and the general gauging procedure of supergravities
is reviewed in some detail.Comment: 101 pages, LaTeX sourc
Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras
In this paper we show that the supergravity equations describing both cosmic
billiards and a large class of black-holes are, generically, both Liouville
integrable as a consequence of the same universal mechanism. This latter is
provided by the Liouville integrable Poissonian structure existing on the dual
Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive
the explicit integration algorithm associated with all symmetric spaces U/H^{*}
relevant to the description of time-like and space-like p-branes. The most
important consequence of our approach is the explicit construction of a
complete set of conserved involutive hamiltonians h_{\alpha} that are
responsible for integrability and provide a new tool to classify flows and
orbits. We believe that these will prove a very important new tool in the
analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references
adde
R--R Scalars, U--Duality and Solvable Lie Algebras
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,
--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.Comment: 17 pages, misprints in Table 2 correcte
Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions
The elliptic genera of two-dimensional N=2 superconformal field theories can
be twisted by the action of the integral Heisenberg group if their U(1) charges
are fractional. The basic properties of the resulting twisted elliptic genera
and the associated twisted Witten indices are investigated with due attention
to their behaviors in orbifoldization. Our findings are illustrated by and
applied to several concrete examples. We give a better understanding of the
duality phenomenon observed long before for certain Landau-Ginzburg models. We
revisit and prove an old conjecture of Witten which states that every ADE
Landau-Ginzburg model and the corresponding minimal model share the same
elliptic genus. Mathematically, we establish ADE generalizations of the
quintuple product identity.Comment: 28 pages; v2 refs adde
Black holes in supergravity and integrability
Stationary black holes of massless supergravity theories are described by
certain geodesic curves on the target space that is obtained after dimensional
reduction over time. When the target space is a symmetric coset space we make
use of the group-theoretical structure to prove that the second order geodesic
equations are integrable in the sense of Liouville, by explicitly constructing
the correct amount of Hamiltonians in involution. This implies that the
Hamilton-Jacobi formalism can be applied, which proves that all such black hole
solutions, including non-extremal solutions, possess a description in terms of
a (fake) superpotential. Furthermore, we improve the existing integration
method by the construction of a Lax integration algorithm that integrates the
second order equations in one step instead of the usual two step procedure. We
illustrate this technology with a specific example.Comment: 44 pages, small typos correcte
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