175 research outputs found
Two-centered magical charge orbits
No full textWe determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product <Q1,Q2>, known to control the mutual nonlocality of the two center
Klein and conformal superspaces, split algebras and spinor orbits
No full text We discuss [Formula: see text] Klein and Klein-conformal superspaces in [Formula: see text] space-time dimensions, realizing them in terms of their functor of points over the split composition algebra [Formula: see text]. We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras. This leads to a natural interpretation of the sections of the spinor bundle in the critical split dimensions [Formula: see text] and [Formula: see text] as [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-conformal superspace structure. </jats:p
Super-Ehlers in any dimension
No full textWe classify the enhanced helicity symmetry of the Ehlers group to extended supergravity theories in any dimension.The vanishing character of the pseudo-Riemannian cosets occurring in this analysis is explained in terms of Poincaré duality .The latter resides in the nature of regularly embedded quotient subgroups which are noncompact rank preservin
On generalized Lemaitre–Tolman–Bondi metric: Fractal matter at the end of matter–antimatter recombination
No full textMany recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On one hand, a first-order perturbative study of matter inhomogeneity returned a partial explanation of dark matter and dark energy, as relativistic effects due to the retarded potentials of far objects. On the other hand, the fractal cosmology, now approximated by a Lemaitre–Tolman–Bondi (LTB) metric, results in distortions of the luminosity distances of SNe Ia, explaining the acceleration as apparent. In this work, we extend the LTB metric to ancient times. The origin of the fractal distribution of matter is explained as the matter remnant after the matter–antimatter recombination epoch. We show that the evolution of such a inhomogeneity necessarily requires a dynamical generalization of LTB, and we propose a particular solution
Special Vinberg cones, invariant admissible cubics and special real manifolds
No full textBy Vinberg theory any homogeneous convex cone V may be realised as the cone of positive Hermitian matrices in a T -algebra of generalised
matrices. The level hypersurfaces V_q ⊂ V of homogeneous cubic polynomials
q with positive definite Hessian (symmetric) form g(q) := − Hess(log(q))|_{T V_q}
are the special real manifolds. Such manifolds occur as scalar manifolds of
the vector multiplets in N = 2, D = 5 supergravity and, through the r-map,
correspond to Kaehler scalar manifolds in N = 2 D = 4 supergravity. We offer
a simplified exposition of the Vinberg theory in terms of Nil-algebras (= the
subalgebras of upper triangular matrices in Vinberg T -algebras) and we use it
to describe all rational functions on a special Vinberg cone that are G_0- or G′-
invariant, where G_0 is the unimodular subgroup of the solvable group G acting
simply transitively on the cone, and G′ is the unipotent radical of G_0. The
results are used to determine G_0- and G′-invariant cubic polynomials q that
are admissible (i.e. such that the hypersurface V_q = {q = 1} ∩ V has positive
definite Hessian form g(q)) for rank 2 and rank 3 special Vinberg cones. We
get in this way examples of continuous families of non-homogeneous special
real manifolds of cohomogeneity less than or equal to two
Symplectic deformations of gauged maximal supergravity
No full textWe identify the space of symplectic deformations of maximal gauged supergravity theories. Coordinates of such space parametrize inequivalent supergravity models with the same gauge group. We apply our procedure to the SO(8) gauging, extending recent analyses. We also study other interesting cases, including Cremmer-Scherk-Schwarz models and gaugings of groups contained in SL(8, R ) and in SU∗(8)
Adams-Iwasawa N=8 Black Holes
No full textWe study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames.We study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames
Quantum klein space and superspace
No full textWe give an algebraic quantization, in the sense of quantum groups, of the complex Minkowski space, and we examine the real forms corresponding to the signatures (3, 1), (2, 2), (4, 0), constructing the corresponding quantum metrics and providing an explicit presentation of the quantized coordinate algebras. In particular, we focus on the Kleinian signature (2, 2). The quantizations of the complex and real spaces come together with a coaction of the quantizations of the respective symmetry groups. We also extend such quantizations to the N = 1 supersetting
LIO-CM. Censimento dei manoscritti della lirica italiana delle origini (dai Siciliani a Dante), I. Austin-Firenze
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