175,316 research outputs found
Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
We review the underlying algebraic structures of supergravity theories with
symmetric scalar manifolds in five and four dimensions, orbits of their
extremal black hole solutions and the spectrum generating extensions of their
U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT)
defined by Euclidean Jordan algebras, J, the spectrum generating symmetry
groups are the conformal groups Conf(J) of J which are isomorphic to their
U-duality groups in four dimensions. Similarly, the spectrum generating
symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J)
associated with J that are isomorphic to their U-duality groups in three
dimensions. We then review the work on spectrum generating symmetries of
spherically symmetric stationary 4D BPS black holes, based on the equivalence
of their attractor equations and the equations for geodesic motion of a
fiducial particle on the target spaces of corresponding 3D supergravity
theories obtained by timelike reduction. We also discuss the connection between
harmonic superspace formulation of 4D, N=2 sigma models coupled to supergravity
and the minimal unitary representations of their isometry groups obtained by
quantizing their quasiconformal realizations. We discuss the relevance of this
connection to spectrum generating symmetries and conclude with a brief summary
of more recent results.Comment: 55 pages; Latex fil
Bifurcations of periodic orbits with spatio-temporal symmetries
Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on bifurcations of group orbits of spatially symmetric equilibria. Two examples, two-dimensional pulsating waves (PW) and three-dimensional alternating pulsating waves (APW), have discrete spatio-temporal symmetries characterized by the cyclic groups Z_n, n=2 (PW) and n=4 (APW). These symmetries force the Poincare' return map M to be the nth iterate of a map G: M=G^n. The group orbits of PW and APW are generated by translations in the horizontal directions and correspond to a circle and a two-torus, respectively. An instability of pulsating waves can lead to solutions that drift along the group orbit, while bifurcations with Floquet multiplier +1 of alternating pulsating waves do not lead to drifting solutions. The third example we consider, alternating rolls, has the spatio-temporal symmetry of alternating pulsating waves as well as being invariant under reflections in two vertical planes. This leads to the possibility of a doubling of the marginal Floquet multiplier and of bifurcation to two distinct types of drifting solutions. We conclude by proposing a systematic way of analysing steady-state bifurcations of periodic orbits with discrete spatio-temporal symmetries, based on applying the equivariant branching lemma to the irreducible representations of the spatio-temporal symmetry group of the periodic orbit, and on the normal form results of Lamb (1996). This general approach is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems
N=4 mechanics, WDVV equations and roots
N=4 superconformal multi-particle quantum mechanics on the real line is
governed by two prepotentials, U and F, which obey a system of partial
differential equations linear in U and generalizing the
Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. Putting U=0 yields a
class of models (with zero central charge) which are encoded by the finite
Coxeter root systems. We extend these WDVV solutions F in two ways: the A_n
system is deformed n-parametrically to the edge set of a general orthocentric
n-simplex, and the BCF-type systems form one-parameter families. A
classification strategy is proposed. A nonzero central charge requires turning
on U in a given F background, which we show is outside of reach of the standard
root-system ansatz for indecomposable systems of more than three particles. In
the three-body case, however, this ansatz can be generalized to establish a
series of nontrivial models based on the dihedral groups I_2(p), which are
permutation symmetric if 3 divides p. We explicitly present their full
prepotentials.Comment: 1+25 pages; v2: major revision (more general analysis, new solutions,
additional references); v3: improvements in sects.5,8,9, refs. adde
The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs
Observations of transversal coronal loop oscillations very often show the
excitation and damping of oscillations in groups of coronal loops rather than
in individual and isolated structures. We present results on the oscillatory
properties (periods, damping rates, and spatial distribution of perturbations)
for resonantly damped oscillations in a system of two inhomogeneous coronal
slabs and compare them to the properties found in single slab loop models. A
system of two identical coronal loops is modeled, in Cartesian geometry, as
being composed by two density enhancements. The linear magnetohydrodynamic
(MHD) wave equations for oblique propagation of waves are solved and the
damping of the different solutions, due to the transversal inhomogeneity of the
density profile, is computed. The physics of the obtained results is analyzed
by an examination of the perturbed physical variables. We find that, due to the
interaction between the loops, the normal modes of oscillation present in a
single slab split into symmetric and antisymmetric oscillations when a system
of two identical slabs is considered. The frequencies of these solutions may
differ from the single slab results when the distance between the loops is of
the order of a few slab widths. Oblique propagation of waves weakens this
interaction, since solutions become more confined to the edges of the slabs.
The damping is strong for surface-like oscillations, while sausage body-like
solutions are unaffected. For some solutions, and small slab separations, the
damping in a system of two loops differs substantially from the damping of a
single loop.Comment: 25 pages, 9 figure
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