801 research outputs found
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition
The statistics of energy levels for a disordered conductor are considered in
the critical energy window near the mobility edge. It is shown that, if
critical wave functions are multifractal, the one-dimensional gas of levels on
the energy axis is ``compressible'', in the sense that the variance of the
level number in an interval is for .
The compressibility, , is given ``exactly'' in terms of the
multifractal exponent at the mobility edge in a -dimensional
system.Comment: 10 pages in REVTeX preprint format; to be published in JETP Letters,
199
Spectral statistics near the quantum percolation threshold
The statistical properties of spectra of a three-dimensional quantum bond
percolation system is studied in the vicinity of the metal insulator
transition. In order to avoid the influence of small clusters, only regions of
the spectra in which the density of states is rather smooth are analyzed. Using
finite size scaling hypothesis, the critical quantum probability for bond
occupation is found to be while the critical exponent for the
divergence of the localization length is estimated as . This
later figure is consistent with the one found within the universality class of
the standard Anderson model.Comment: REVTeX, 4 pages, 5 figures, all uuencoded, accepted for publication
in PRB (Rapid Communication
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
We study the symmetries of pure N=2 supergravity in D=4. As is known, this
theory reduced on one Killing vector is characterised by a non-linearly
realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We
consider the BPS brane solutions of the theory preserving half of the
supersymmetry and the action of SU(2,1) on them. Furthermore we provide
evidence that the theory exhibits an underlying algebraic structure described
by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from
the correspondence between the bosonic space-time fields of N=2 supergravity in
D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++},
as well as from the fact that the structure of BPS brane solutions is neatly
encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a
regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on
brane physics.Comment: 70 pages, final version published in JHE
Mesoscopic motion of atomic ions in magnetic fields
We introduce a semiclassical model for moving highly excited atomic ions in a
magnetic field which allows us to describe the mixing of the Landau orbitals of
the center of mass in terms of the electronic excitation and magnetic field.
The extent of quantum energy flow in the ion is investigated and a crossover
from localization to delocalization with increasing center of mass energy is
detected. It turns out that our model of the moving ion in a magnetic field is
closely connected to models for transport in disordered finite-size wires.Comment: 4 pages, 2 figures, subm. to Phys.Rev.A, Rap.Co
Hyperbolic billiards of pure D=4 supergravities
We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz
(BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as
for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find
that just as for the cases N=0 and N=8 investigated previously, these billiards
can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody
algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature
arises, however, which is that the relevant Kac-Moody algebra can be the
Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and
N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of
this property is provided by showing that the data relevant for determining the
billiards are the restricted root system and the maximal split subalgebra of
the finite-dimensional real symmetry algebra characterizing the toroidal
reduction to D=3 spacetime dimensions. To summarize: split symmetry controls
chaos.Comment: 21 page
Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology
We re-examine previously found cosmological solutions to eleven-dimensional
supergravity in the light of the E_{10}-approach to M-theory. We focus on the
solutions with non zero electric field determined by geometric configurations
(n_m, g_3), n\leq 10. We show that these solutions are associated with rank
regular subalgebras of E_{10}, the Dynkin diagrams of which are the (line)
incidence diagrams of the geometric configurations. Our analysis provides as a
byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group
of E_{10}.Comment: 48 pages, 27 figures, 5 tables, references added, typos correcte
Band Distributions for Quantum Chaos on the Torus
Band distributions (BDs) are introduced describing quantization in a toral
phase space. A BD is the uniform average of an eigenstate phase-space
probability distribution over a band of toral boundary conditions. A general
explicit expression for the Wigner BD is obtained. It is shown that the Wigner
functions for {\em all} of the band eigenstates can be reproduced from the
Wigner BD. Also, BDs are shown to be closer to classical distributions than
eigenstate distributions. Generalized BDs, associated with sets of adjacent
bands, are used to extend in a natural way the Chern-index characterization of
the classical-quantum correspondence on the torus to arbitrary rational values
of the scaled Planck constant.Comment: 12 REVTEX page
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability
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