5,263 research outputs found
String Geometry and the Noncommutative Torus
We construct a new gauge theory on a pair of d-dimensional noncommutative
tori. The latter comes from an intimate relationship between the noncommutative
geometry associated with a lattice vertex operator algebra A and the
noncommutative torus. We show that the (truncated) tachyon subalgebra of A is
naturally isomorphic to a class of twisted modules representing quantum
deformations of the algebra of functions on the torus. We construct the
corresponding even real spectral triples and determine their Morita equivalence
classes using string duality arguments. These constructions yield simple proofs
of the O(d,d;Z) Morita equivalences between -dimensional noncommutative tori
and give a natural physical interpretation of them in terms of the target space
duality group of toroidally compactified string theory. We classify the
automorphisms of the twisted modules and construct the most general gauge
theory which is invariant under the automorphism group. We compute bosonic and
fermionic actions associated with these gauge theories and show that they are
explicitly duality-symmetric. The duality-invariant gauge theory is manifestly
covariant but contains highly non-local interactions. We show that it also
admits a new sort of particle-antiparticle duality which enables the
construction of instanton field configurations in any dimension. The duality
non-symmetric on-shell projection of the field theory is shown to coincide with
the standard non-abelian Yang-Mills gauge theory minimally coupled to massive
Dirac fermion fields.Comment: 37 pages, LaTeX. Major revisions in section 3. Other minor revisions
in the rest of the paper, references adde
Algebraic deformations of toric varieties I. General constructions
We construct and study noncommutative deformations of toric varieties by
combining techniques from toric geometry, isospectral deformations, and
noncommutative geometry in braided monoidal categories. Our approach utilizes
the same fan structure of the variety but deforms the underlying embedded
algebraic torus. We develop a sheaf theory using techniques from noncommutative
algebraic geometry. The cases of projective varieties are studied in detail,
and several explicit examples are worked out, including new noncommutative
deformations of Grassmann and flag varieties. Our constructions set up the
basic ingredients for thorough study of instantons on noncommutative toric
varieties, which will be the subject of the sequel to this paper.Comment: 54 pages; v2: Presentation of Grassmann and flag varieties improved,
minor corrections; v3: Presentation of some parts streamlined, minor
corrections, references added; final version to appear in Advances in
Mathematic
Algebraic deformations of toric varieties II. Noncommutative instantons
We continue our study of the noncommutative algebraic and differential
geometry of a particular class of deformations of toric varieties, focusing on
aspects pertinent to the construction and enumeration of noncommutative
instantons on these varieties. We develop a noncommutative version of twistor
theory, which introduces a new example of a noncommutative four-sphere. We
develop a braided version of the ADHM construction and show that it
parametrizes a certain moduli space of framed torsion free sheaves on a
noncommutative projective plane. We use these constructions to explicitly build
instanton gauge bundles with canonical connections on the noncommutative
four-sphere that satisfy appropriate anti-selfduality equations. We construct
projective moduli spaces for the torsion free sheaves and demonstrate that they
are smooth. We define equivariant partition functions of these moduli spaces,
finding that they coincide with the usual instanton partition functions for
supersymmetric gauge theories on C^2.Comment: 62 pages; v2: typos corrected, references updated; Final version to
be published in Advances in Theoretical and Mathematical Physic
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
We construct an approximation to field theories on the noncommutative torus
based on soliton projections and partial isometries which together form a
matrix algebra of functions on the sum of two circles. The matrix quantum
mechanics is applied to the perturbative dynamics of scalar field theory, to
tachyon dynamics in string field theory, and to the Hamiltonian dynamics of
noncommutative gauge theory in two dimensions. We also describe the adiabatic
dynamics of solitons on the noncommutative torus and compare various classes of
noncommutative solitons on the torus and the plane.Comment: 70 pages, 4 figures; v2: References added and update
Signatures of Incomplete Paschen-Back Splitting in the Polarization Profiles of the He I 10830 multiplet
We investigate the formation of polarization profiles induced by a magnetic
field in the He I multiplet at 1083,0 nm . Our analysis considers the Zeeman
splitting in the incomplete Paschen-Back regime. The effects turn out to be
important and produce measurable signatures on the profiles, even for fields
significantly weaker than the level-crossing field (400 G). When compared
to profiles calculated with the usual linear Zeeman effect, the incomplete
Paschen-Back profiles exhibit the following conspicuous differences: a) a
non-Doppler blueshift of the Stokes V zero-crossing wavelength of the blue
component; b) area and peak asymmetries, even in the absence of velocity and
magnetic gradients; c) a 25% reduction in the amplitude of the red
component. These features do not vanish in the weak field limit. The spectral
signatures that we analyze in this paper may be found in previous observations
published in the literature.Comment: Accepted for publication in The Astrophysical Journa
Polynomial Approximants for the Calculation of Polarization Profiles in the \ion{He}{1} 10830 \AA Multiplet
The \ion{He}{1} multiplet at 10830 \AA is formed in the incomplete
Paschen-Back regime for typical conditions found in solar and stellar
atmospheres. The positions and strengths of the various components that form
the Zeeman structure of this multiplet in the Paschen-Back regime are
approximated here by polynomials. The fitting errors are smaller than
m\AA in the component positions and in the relative
strengths. The approximant polynomials allow for a very fast implementation of
the incomplete Paschen-Back regime in numerical codes for the synthesis and
inversion of polarization profiles in this important multiplet.Comment: ApJ Supplements (in press
Isotropic inelastic and superelastic collisional rates in a multiterm atom
The spectral line polarization of the radiation emerging from a magnetized
astrophysical plasma depends on the state of the atoms within the medium, whose
determination requires considering the interactions between the atoms and the
magnetic field, between the atoms and photons (radiative transitions), and
between the atoms and other material particles (collisional transitions). In
applications within the framework of the multiterm model atom (which accounts
for quantum interference between magnetic sublevels pertaining either to the
same J-level or to different J-levels within the same term) collisional
processes are generally neglected when solving the master equation for the
atomic density matrix. This is partly due to the lack of experimental data
and/or of approximate theoretical expressions for calculating the collisional
transfer and relaxation rates (in particular the rates for interference between
sublevels pertaining to different J-levels, and the depolarizing rates due to
elastic collisions). In this paper we formally define and investigate the
transfer and relaxation rates due to isotropic inelastic and superelastic
collisions that enter the statistical equilibrium equations of a multiterm
atom. Under the hypothesis that the atom-collider interaction can be described
by a dipolar operator, we provide expressions that relate the collisional rates
for interference between different J-levels to the usual collisional rates for
J-level populations. Finally, we apply the general equations to the case of a
two-term atom with unpolarized lower term, illustrating the impact of inelastic
and superelastic collisions on scattering polarization through radiative
transfer calculations in a slab of stellar atmospheric plasma anisotropically
illuminated by the photospheric radiation field.Comment: Accepted for publication in Astronomy & Astrophysic
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