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

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

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

A Matrix Model for \nu_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States

We propose a matrix model to describe a class of fractional quantum Hall (FQH) states for a system of (N_1+N_2) electrons with filling factor more general than in the Laughlin case. Our model, which is developed for FQH states with filling factor of the form \nu_{k_1k_2}=\frac{k_1+k_2}{k_1k_2} (k_1 and k_2 odd integers), has a U(N_1)\times U(N_2) gauge invariance, assumes that FQH fluids are composed of coupled branches of the Laughlin type, and uses ideas borrowed from hierarchy scenarios. Interactions are carried, amongst others, by fields in the bi-fundamentals of the gauge group. They simultaneously play the role of a regulator, exactly as does the Polychronakos field. We build the vacuum configurations for FQH states with filling factors given by the series \nu_{p_1p_2}=\frac{p_2}{p_1p_2-1}, p_1 and p_2 integers. Electrons are interpreted as a condensate of fractional D0-branes and the usual degeneracy of the fundamental state is shown to be lifted by the non-commutative geometry behaviour of the plane. The formalism is illustrated for the state at \nu={2/5}.Comment: 40 pages, 1 figure, clarifications and references adde

A Matrix Model for the Null-Brane

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied.Comment: 26 pages, LaTeX; references adde

World-sheet duality for D-branes with travelling waves

We study D-branes with plane waves of arbitrary profiles as examples of time-dependent backgrounds in string theory. We show how to reproduce the quantum mechanical (one-to-one) open-string S-matrix starting from the closed-string boundary state for the D-branes, thereby establishing the channel duality of this calculation. The required Wick rotation to a Lorentzian worldsheet singles out as 'prefered' time coordinate the open-string light-cone time.Comment: 17 pages, Latex file, uses JHEP3.cls, two figures. Added references and corrected two typo