14 research outputs found
Noncommutative Quantum Mechanics and rotating frames
We study the effect of noncommutativity of space on the physics of a quantum
interferometer located in a rotating disk in a gauge field background. To this
end, we develop a path-integral approach which allows defining an effective
action from which relevant physical quantities can be computed as in the usual
commutative case. For the specific case of a constant magnetic field, we are
able to compute, exactly, the noncommutative Lagrangian and the associated
shift on the interference pattern for any value of .Comment: 17 pages, presentation improved, references added. To appear in
Physical Review
Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
We discuss different dualities of QHE in the framework of the noncommutative
Chern-Simons theory. First, we consider the Morita or T-duality transformation
on the torus which maps the abelian noncommutative CS description of QHE on the
torus into the nonabelian commutative description on the dual torus. It is
argued that the Ruijsenaars integrable many-body system provides the
description of the QHE with finite amount of electrons on the torus. The new
IIB brane picture for the QHE is suggested and applied to Jain and generalized
hierarchies. This picture naturally links 2d -model and 3d CS
description of the QHE. All duality transformations are identified in the brane
setup and can be related with the mirror symmetry and S duality. We suggest a
brane interpretation of the plateu transition in IQHE in which a critical point
is naturally described by WZW model.Comment: 31 pages, 4 figure
BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography
In this paper, we propose a new approach to study the BPS dynamics in N=4
supersymmetric U(N) Yang-Mills theory on R X S^3, in order to better understand
the emergence of gravity in the gauge theory. Our approach is based on
supersymmetric, space-filling Q-balls with R-charge, which we call R-balls. The
usual collective coordinate method for non-topological scalar solitons is
applied to quantize the half and quarter BPS R-balls. In each case, a different
quantization method is also applied to confirm the results from the collective
coordinate quantization. For finite N, the half BPS R-balls with a U(1)
R-charge have a moduli space which, upon quantization, results in the states of
a quantum Hall droplet with filling factor one. These states are known to
correspond to the ``sources'' in the Lin-Lunin-Maldacena geometries in IIB
supergravity. For large N, we find a new class of quarter BPS R-balls with a
non-commutativity parameter. Quantization on the moduli space of such R-balls
gives rise to a non-commutative Chern-Simons matrix mechanics, which is known
to describe a fractional quantum Hall system. In view of AdS/CFT holography,
this demonstrates a profound connection of emergent quantum gravity with
non-commutative geometry, of which the quantum Hall effect is a special case.Comment: 42 pages, 2 figures; v3: a new paragraph on counting unbroken susy of
NC R-balls and references adde
Jain States in a Matrix Theory of the Quantum Hall Effect
The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension
of Susskind's noncommutative approach. The theory describes D0-branes,
nonrelativistic particles with matrix coordinates and gauge symmetry, that
realize a matrix generalization of the quantum Hall effect. Matrix ground
states obtained by suitable projections of higher Landau levels are found to be
in one-to-one correspondence with the expected Laughlin and Jain hierarchical
states. The Jain composite-fermion construction follows by gauge invariance via
the Gauss law constraint. In the limit of commuting, ``normal'' matrices the
theory reduces to eigenvalue coordinates that describe realistic electrons with
Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier
noncommutative approaches and could provide another effective theory of the
fractional Hall effect.Comment: 35 pages, 3 figure
NC Effective Gauge Model for Multilayer FQH States
We develop an effective field model for describing FQH states with rational
filling factors that are not of Laughlin type. These kinds of systems, which
concern single layer hierarchical states and multilayer ones, were observed
experimentally; but have not yet a satisfactory non commutative effective field
description like in the case of Susskind model. Using brane analysis and
fiber bundle techniques, we first classify such states in terms of
representations characterized, amongst others, by the filling factor of the
layers; but also by proper subgroups of the underlying gauge symmetry.
Multilayer states in the lowest Landau level are interpreted in terms of
systems of branes; but hierarchical ones are realized as Fiber bundles on
which we construct explicitly. In this picture, Jain and Haldane series
are recovered as special cases and have a remarkable interpretation in terms of
Fiber bundles with specific intersection matrices. We also derive the general
NC commutative effective field and matrix models for FQH states, extending
Susskind theory, and give the general expression of the rational filling
factors as well as their non abelian gauge symmetries.Comment: 54 pages 11 figures, LaTe
Noncommutative Fluids
We review the connection between noncommutative gauge theory, matrix models
and fluid mechanical systems. The noncommutative Chern-Simons description of
the quantum Hall effect and bosonization of collective fermion states are used
as specific examples.Comment: To appear in "Seminaire Poincare X", Institut Henri Poincare, Paris;
references adde
3-Form Induced Potentials, Dilaton Stabilization, and Running Moduli
We study the potential induced by imaginary self-dual 3-forms in compactifications of string theory and the cosmological evolution associated with it. The potential contains exponentials of the volume moduli of the compactification, and we demonstrate that the exponential form of the potential leads to a power law for the scale factor of the universe. This power law does not support accelerated expansion. We explain this result in terms of supersymmetry and comment on corrections to the potential that could lead to inflation or quintessence