1,079 research outputs found
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters and .Comment: 9 pages, RevTeX4, references added, small changes in the tex
The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
We present an exact description of the metric on the moduli space of vacua
and the spectrum of massive states for four dimensional N=2 supersymmetric
SU(n) gauge theories. The moduli space of quantum vacua is identified with the
moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde
Varieties of vacua in classical supersymmetric gauge theories
We give a simple description of the classical moduli space of vacua for
supersymmetric gauge theories with or without a superpotential. The key
ingredient in our analysis is the observation that the lagrangian is invariant
under the action of the complexified gauge group \Gc. From this point of view
the usual -flatness conditions are an artifact of Wess--Zumino gauge. By
using a gauge that preserves \Gc invariance we show that every constant
matter field configuration that extremizes the superpotential is \Gc
gauge-equivalent (in a sense that we make precise) to a unique classical
vacuum. This result is used to prove that in the absence of a superpotential
the classical moduli space is the algebraic variety described by the set of all
holomorphic gauge-invariant polynomials. When a superpotential is present, we
show that the classical moduli space is a variety defined by imposing
additional relations on the holomorphic polynomials. Many of these points are
already contained in the existing literature. The main contribution of the
present work is that we give a careful and self-contained treatment of limit
points and singularities.Comment: 14 pages, LaTeX (uses revtex.sty
Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with supersymmetry in terms of gauge-invariant variables is presented,
generalizing earlier work on nonsupersymmetric gauge theories. Special
attention is paid to the volume measure of integration (over the gauge orbit
space of the fields) which occurs in the inner product for the wave functions
and arguments relating it to the renormalization of the Chern-Simons level
number and to mass-gaps in the spectrum of the Hamiltonians are presented. The
expression for the integration measure is consistent with the absence of mass
gap for theories with extended supersymmetry (in the absence of additional
matter hypermultiplets and/or Chern-Simons couplings), while for the minimally
supersymmetric case, there is a mass-gap, the scale of which is set by a
renormalized level number, in agreement with indications from existing
literature. The realization of the supersymmetry algebra and the Hamiltonian in
terms of the gauge invariant variables is also presented.Comment: 31 pages, References added, typos correcte
Giant magnon bound states from strongly coupled N=4 SYM
We calculate in a very simple way the spectrum of giant magnon bound states
at strong coupling in N=4 SYM, by utilizing the description of the field theory
vacuum in terms of a condensate of eigenvalues of commuting matrices. We
further show that these calculations can be understood in terms of the central
charge extension that permits the calculation of BPS masses in the Coulomb
branch of N=4 SYM. This paper shows further evidence that the strong coupling
expansion of the maximally supersymmetric Yang-Mills theory in four dimensions
can be done systematically from first principles, without the assumption of
integrability.Comment: 19 pages, uses revte
Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
We study four dimensional supersymmetric gauge theories with matter
multiplets. For all such models for which the gauge group is , we derive
the exact metric on the moduli space of quantum vacua and the exact spectrum of
the stable massive states. A number of new physical phenomena occur, such as
chiral symmetry breaking that is driven by the condensation of magnetic
monopoles that carry global quantum numbers. For those cases in which conformal
invariance is broken only by mass terms, the formalism automatically gives
results that are invariant under electric-magnetic duality. In one instance,
this duality is mixed in an interesting way with triality.Comment: 89 page
Horizons and plane waves: A review
We review the attempts to construct black hole/string solutions in
asymptotically plane wave spacetimes. First, we demonstrate that geometries
admitting a covariantly constant null Killing vector cannot admit event
horizons, which implies that pp-waves can't describe black holes. However,
relaxing the symmetry requirements allows us to generate solutions which do
possess regular event horizons while retaining the requisite asymptotic
properties. In particular, we present two solution generating techniques and
use them to construct asymptotically plane wave black string/brane geometries.Comment: 15 pages, harvmac. Review to appear in Modern Physics Letters A v2:
added reference
Symplectic SUSY Gauge Theories with Antisymmetric Matter
We investigate the confining phase vacua of supersymmetric Sp(2\NC) gauge
theories that contain matter in both fundamental and antisymmetric
representations. The moduli spaces of such models with \NF=3 quark flavors
and \NA=1 antisymmetric field are analogous to that of SUSY QCD with
\NF=\NC+1 flavors. In particular, the forms of their quantum superpotentials
are fixed by classical constraints. When mass terms are coupled to
W_{(\NF=3,\NA=1)} and heavy fields are integrated out, complete towers of
dynamically generated superpotentials for low energy theories with fewer
numbers of matter fields can be derived. Following this approach, we deduce
exact superpotentials in and theories which cannot be
determined by symmetry considerations or integrating in techniques. Building
upon these simple symplectic group results, we also examine the ground state
structures of several and models. We
emphasize that the top-down approach may be used to methodically find dynamical
superpotentials in many other confining supersymmetric gauge theories.Comment: 21 pages, Revte
Emergent Geometry and Quantum Gravity
We explain how quantum gravity can be defined by quantizing spacetime itself.
A pinpoint is that the gravitational constant G = L_P^2 whose physical
dimension is of (length)^2 in natural unit introduces a symplectic structure of
spacetime which causes a noncommutative spacetime at the Planck scale L_P. The
symplectic structure of spacetime M leads to an isomorphism between symplectic
geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of
symplectic structure \omega in terms of electromagnetic fields F=dA are
transformed into those of Riemannian metric g. This approach for quantum
gravity allows a background independent formulation where spacetime as well as
matter fields is equally emergent from a universal vacuum of quantum gravity
which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page
Solving Four Dimensional Field Theories with the Dirichlet Fivebrane
The realization of four dimensional super Yang-Mills theories in
terms of a single Dirichlet fivebrane in type IIB string theory is considered.
A classical brane computation reproduces the full quantum low energy effective
action. This result has a simple explanation in terms of mirror symmetry.Comment: Final version to appear in Phys. Rev.
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