231 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
ALE manifolds and Conformal Field Theory
We address the problem of constructing the family of (4,4) theories
associated with the sigma-model on a parametrized family of
Asymptotically Locally Euclidean (ALE) manifolds. We rely on the ADE
classification of these manifolds and on their construction as HyperK\"ahler
quotients, due to Kronheimer.
So doing we are able to define the family of (4,4) theories corresponding to
a family of ALE manifolds as the deformation of a solvable
orbifold conformal field-theory, being a
Kleinian group. We discuss the relation among the algebraic structure
underlying the topological and metric properties of self-dual 4-manifolds and
the algebraic properties of non-rational (4,4)-theories admitting an infinite
spectrum of primary fields. In particular, we identify the Hirzebruch signature
with the dimension of the local polynomial ring {\cal R}=\o {{\bf
C}[x,y,z]}{\partial W} associated with the ADE singularity, with the number of
non-trivial conjugacy classes in the corresponding Kleinian group and with the
number of short representations of the (4,4)-theory minus four.Comment: 48 pages, Latex, SISSA/44/92/EP, IFUM/443/F
Supersymmetry and First Order Equations for Extremal States: Monopoles, Hyperinstantons, Black-Holes and p-Branes
In this lecture I review recent results on the first order equations
describing BPS extremal states, in particular N=2 extremal black-holes. The
role of special geometry is emphasized also in the rigid theory and a
comparison is drawn with the supersymmetric derivation of instantons and
hyperinstantons in topological field theories. Work in progress on the
application of solvable Lie algebras to the discussion of BPS states in
maximally extended supergravities is outlined.Comment: LaTeX, {article.sty, espcrc2.sty} 11 twocolumn pages. Invited Seminar
given at Santa Margerita Conference on Contrained Dynamics and Quantum
Gravity September 1995. In the replaced version misprints have been corrected
and some sentences have been modifie
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
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