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 ${\bf F}_2 = SU(3)/U(1)\times U(1)$ 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 ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ 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 $\nu =1$. 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 $N-$dimensional Lobachewski spaces ${\cal L}_N$. 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 $N>1$ 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 ${\cal L}_N$, 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 $m_c$, 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 $1/2\pi\alpha'$ 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 $\pi/2$ 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 $R^{1,d}/Z_2$ orbifold, where $Z_2$ 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 $R^{1,d}$, 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