539 research outputs found
On the Embedding of Space-Time Symmetries into Simple Superalgebras
We explore the embedding of Spin groups of arbitrary dimension and signature
into simple superalgebras in the case of extended supersymmetry. The
R-symmetry, which generically is not compact, can be chosen compact for all the
cases that are congruent mod 8 to the physical conformal algebra so(,2),
. An grading of the superalgebra is found in all cases.
Central extensions of super translation algebras are studied in this framework.Comment: AMS LaTeX, 16 page
Generalized dimensional reduction of supergravity with eight supercharges
We describe some recent investigation about the structure of generic D=4,5
theories obtained by generalized dimensional reduction of D=5,6 theories with
eight supercharges. We relate the Scherk-Schwarz reduction to a special class
of N=2 no-scale gauged supergravities.Comment: Contribution to the proceedings of ``NathFest'' at PASCOS conference,
Northeastern University, Boston, Ma, August 200
SU(2) Poisson-Lie T duality
Poisson-Lie target space duality is a framework where duality transformations
are properly defined. In this letter we investigate the pair of sigma models
defined by the double SO(3,1) in the Iwasawa decomposition.Comment: 12 pages, 1 figur
On the deformation quantization of affine algebraic varieties
We compute an explicit algebraic deformation quantization for an affine
Poisson variety described by an ideal in a polynomial ring, and inheriting its
Poisson structure from the ambient space.Comment: AMS-LaTeX, 20 page
On the Super Higgs Effect in Extended Supergravity
We consider the reduction of supersymmetry in N-extended four dimensional
supergravity via the super Higgs mechanism in theories without cosmological
constant. We provide an analysis largely based on the properties of long and
short multiplets of Poincare' supersymmetry. Examples of the super Higgs
phenomenon are realized in spontaneously broken N=8 supergravity through the
Scherk-Schwarz mechanism and in superstring compactification in presence of
brane fluxes. In many models the massive vectors count the difference in number
of the translation isometries of the scalar sigma-model geometries in the
broken and unbroken phase.Comment: Version to appear on Nuclear Physics
Special geometry for arbitrary signatures
In this paper we generalize special geometry to arbitrary signatures in
target space. We formulate the definitions in a precise mathematical setting
and give a translation to the coordinate formalism used in physics. For the
projective case, we first discuss in detail projective Kaehler manifolds,
appearing in N=1 supergravity. We develop a new point of view based on the
intrinsic construction of the line bundle. The topological properties are then
derived and the Levi-Civita connection in the projective manifold is obtained
as a particular projection of a Levi-Civita connection in a `mother' manifold
with one extra complex dimension. The origin of this approach is in the
superconformal formalism of physics, which is also explained in detail.
Finally, we specialize these results to projective special Kaehler manifolds
and provide explicit examples with different choices of signature.Comment: LaTeX, 83 pages; v2: typos corrected, version to be published in
Handbook of pseudo-Riemannian Geometry and Supersymmetry, IRMA Lectures in
Mathematics and Theoretical Physic
Axion gauge symmetries and generalized Chern-Simons terms in N=1 supersymmetric theories
We compute the form of the Lagrangian of N=1 supersymmetric theories with
gauged axion symmetries. It turns out that there appear generalized
Chern-Simons terms that were not considered in previous superspace formulations
of general N=1 theories. Such gaugings appear in supergravities arising from
flux compactifications of superstrings, as well as from Scherk-Schwarz
generalized dimensional reduction in M-theory. We also present the dual
superspace formulation where axion chiral multiplets are dualized into linear
multiplets.Comment: References added and few misprints correcte
No-scale D=5 supergravity from Scherk-Schwarz reduction of D=6 theories
We perform a generalized dimensional reduction of six dimensional
supergravity theories to five dimensions. We consider the minimal and
the maximal theories. In each case the reduction allows us to obtain
gauged supergravities of no-scale type in dimension five with gauge groups that
escape previous classifications. In the minimal case, the geometric data of the
reduced theory correspond to particular cases of the D=5 real special geometry.
In the maximal case we find a four parameter solution which allows partial
breaking of supersymmetry.Comment: AMS-LaTeX 16 pages. A reference added, some minor changes performe
Rigorous steps towards holography in asymptotically flat spacetimes
Scalar QFT on the boundary at null infinity of a general
asymptotically flat 4D spacetime is constructed using the algebraic approach
based on Weyl algebra associated to a BMS-invariant symplectic form. The
constructed theory is invariant under a suitable unitary representation of the
BMS group with manifest meaning when the fields are interpreted as suitable
extensions to of massless minimally coupled fields propagating in the
bulk. The analysis of the found unitary BMS representation proves that such a
field on coincides with the natural wave function constructed out of
the unitary BMS irreducible representation induced from the little group
, the semidirect product between SO(2) and the two dimensional
translational group. The result proposes a natural criterion to solve the long
standing problem of the topology of BMS group. Indeed the found natural
correspondence of quantum field theories holds only if the BMS group is
equipped with the nuclear topology rejecting instead the Hilbert one.
Eventually some theorems towards a holographic description on of QFT in
the bulk are established at level of algebras of fields for strongly
asymptotically predictable spacetimes. It is proved that preservation of a
certain symplectic form implies the existence of an injective -homomorphism
from the Weyl algebra of fields of the bulk into that associated with the
boundary . Those results are, in particular, applied to 4D Minkowski
spacetime where a nice interplay between Poincar\'e invariance in the bulk and
BMS invariance on the boundary at is established at level of QFT. It
arises that the -homomorphism admits unitary implementation and Minkowski
vacuum is mapped into the BMS invariant vacuum on .Comment: 62 pages, amslatex, xy package; revised section 2 and the
conclusions; corrected some typos; added some references; accepted for
pubblication on Rev. Math. Phy
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