106 research outputs found
Oscillator potential for the four-dimensional Hall effect
We suggest the exactly solvable model of oscillator on the four-dimensional
sphere interacting with the SU(2) Yang monopole. We show, that the properties
of the model essentially depend on the monopole charge.Comment: 4 page
Quantum Hall Effect on the Flag Manifold F_2
The Landau problem on the flag manifold
is analyzed from an algebraic point of view. The involved magnetic background
is induced by two U(1) abelian connections. In quantizing the theory, we show
that the wavefunctions, of a non-relativistic particle living on ,
are the SU(3) Wigner -functions satisfying two constraints. Using the
algebraic and geometrical structures, we derive the Landau
Hamiltonian as well as its energy levels. The Lowest Landau level (LLL)
wavefunctions coincide with the coherent states for the mixed SU(3)
representations. We discuss the quantum Hall effect for a filling factor . where the obtained particle density is constant and finite for a strong
magnetic field. In this limit, we also show that the system behaves like an
incompressible fluid. We study the semi-classical properties of the system
confined in LLL. These will be used to discuss the edge excitations and
construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected,
version to appear in IJMP
Quantum Oscillator on \DC P^n in a constant magnetic field
We construct the quantum oscillator interacting with a constant magnetic
field on complex projective spaces \DC P^N, as well as on their non-compact
counterparts, i. e. the dimensional Lobachewski spaces . We
find the spectrum of this system and the complete basis of wavefunctions.
Surprisingly, the inclusion of a magnetic field does not yield any qualitative
change in the energy spectrum. For the magnetic field does not break the
superintegrability of the system, whereas for N=1 it preserves the exact
solvability of the system.
We extend this results to the cones constructed over \DC P^N and , and perform the (Kustaanheimo-Stiefel) transformation of these systems
to the three-dimensional Coulomb-like systems.Comment: 9 pages, 1 figur
Relativistic D-brane Scattering is Extremely Inelastic
We study the effects of quantum production of open strings on the
relativistic scattering of D-branes. We find strong corrections to the brane
trajectory from copious production of highly-excited open strings, whose
typical oscillator level is proportional to the square of the rapidity. In the
corrected trajectory, the branes rapidly coincide and remain trapped in a
configuration with enhanced symmetry. This is a purely stringy effect which
makes relativistic brane collisions exceptionally inelastic. We trace this
effect to velocity-dependent corrections to the open-string mass, which render
open strings between relativistic D-branes surprisingly light. We observe that
pair-creation of open strings could play an important role in cosmological
scenarios in which branes approach each other at very high speeds.Comment: 30 pages; added references and a comment about velocity-dependent
masse
Self-gravitating Yang Monopoles in all Dimensions
The (2k+2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k)
(or SU(2) for k=2 and SU(3) for k=3) are shown to admit a family of
spherically-symmetric magnetic monopole solutions, for both zero and non-zero
cosmological constant Lambda, characterized by a mass m and a magnetic-type
charge. The k=1 case is the Reissner-Nordstrom black hole. The k=2 case yields
a family of self-gravitating Yang monopoles. The asymptotic spacetime is
Minkowski for Lambda=0 and anti-de Sitter for Lambda<0, but the total energy is
infinite for k>1. In all cases, there is an event horizon when m>m_c, for some
critical mass , which is negative for k>1. The horizon is degenerate when
m=m_c, and the near-horizon solution is then an adS_2 x S^{2k} vacuum.Comment: 16 pp. Extensive revision to include case of non-zero cosmological
constant and implications for adS/CFT. Numerous additional reference
A Matrix Big Bang
The light-like linear dilaton background represents a particularly simple
time-dependent 1/2 BPS solution of critical type IIA superstring theory in ten
dimensions. Its lift to M-theory, as well as its Einstein frame metric, are
singular in the sense that the geometry is geodesically incomplete and the
Riemann tensor diverges along a light-like subspace of codimension one. We
study this background as a model for a big bang type singularity in string
theory/M-theory. We construct the dual Matrix theory description in terms of a
(1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given
by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a
framework in which the physics of the singularity appears to be under control.Comment: 25 pages, LaTeX; v2: discussion of singularity of Einstein frame
metric added, references adde
Supersymmetric Boost on Intersecting D-branes
We study the effect of the Born-Infeld electric field on the supersymmetric
configuration of various composite D-branes. We show that the generic values of
the electric field do not affect the supersymmetry but, as it approaches
keeping the magnetic field finite, various combinations of the
magnetic fields allow up to 8 supersymmetries. We also explore the unbroken
supersymmetries for two intersecting D-strings which are in uniform or relative
motion. For a finite uniform Lorentz boost, 16 supersymmetries are guaranteed
only when they are parallel. For an infinite one, 8 supersymmetries are
preserved only when both the D-strings are oriented to the forward or backward
direction of the boost. Under a finite relative boost, 8 supersymmetries are
preserved only when the intersecting angle is less than and the
intersecting point moves at the speed of light. As for an infinite relative
boost, 8 supersymmetries are preserved regardless of the values of the
intersecting angle.Comment: 27 pages using REVTeX4, 7 figure
Numerical Study of Cosmic Censorship in String Theory
Recently Hertog, Horowitz, and Maeda have argued that cosmic censorship can
be generically violated in string theory in anti-de Sitter spacetime by
considering a collapsing bubble of a scalar field whose mass saturates the
Breitenlohner-Freedman bound. We study this system numerically and find that
for various choices of initial data black holes form rather than naked
singularities, implying that in these cases cosmic censorship is upheld.Comment: 16 pages, latex, 10 figures, uses JHEP.cls, v2: minor changes,
version to be published in JHE
The Taming of Closed Time-like Curves
We consider a orbifold, where acts by time and space
reversal, also known as the embedding space of the elliptic de Sitter space.
The background has two potentially dangerous problems: time-nonorientability
and the existence of closed time-like curves. We first show that closed causal
curves disappear after a proper definition of the time function. We then
consider the one-loop vacuum expectation value of the stress tensor. A naive
QFT analysis yields a divergent result. We then analyze the stress tensor in
bosonic string theory, and find the same result as if the target space would be
just the Minkowski space , suggesting a zero result for the
superstring. This leads us to propose a proper reformulation of QFT, and
recalculate the stress tensor. We find almost the same result as in Minkowski
space, except for a potential divergence at the initial time slice of the
orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that
it is possible to define local S-matrices, even if the spacetime is globally
time-nonorientable.Comment: 37 pages, LaTeX2e, uses amssymb, amsmath and epsf macros, 8 eps and 3
ps figures; (v2): Two additional comments + one reference added; (v3):
corrections in discussion of CTCs + some clarification
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