8,729 research outputs found
A cellular topological field theory
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect to composition of cobordisms
Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation
In this paper, after a brief review of the general theory of dispersive waves
in dissipative media, we present a complete discussion of the dispersion
relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat
equations. Consequently, we provide a complete characterization of the group
and phase velocities for these two cases, together with some non-trivial
remarks on the nature of wave dispersion in fractional models.Comment: 18 pages, 7 figure
On the convergence of Magnetorotational turbulence in stratified isothermal shearing boxes
We consider the problem of convergence in stratified isothermal shearing
boxes with zero net magnetic flux. We present results with the highest
resolution to-date--up to 200 grid-point per pressure scale height--that show
no clear evidence of convergence. Rather, the Maxwell stresses continue to
decrease with increasing resolution. We propose some possible scenarios to
explain the lack of convergence based on multi-layer dynamo systems.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter
Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables
We study the differential geometry of principal G-bundles whose base space is
the space of free paths (loops) on a manifold M. In particular we consider
connections defined in terms of pairs (A,B), where A is a connection for a
fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures,
parallel transports and holonomies are computed and their expressions in local
coordinates are exhibited. When the 2-form B is given by the curvature of A,
then the so-called non-abelian Stokes formula follows.
For a generic 2-form B, we distinguish the cases when the parallel transport
depends on the whole path of paths and when it depends only on the spanned
surface. In particular we discuss generalizations of the non-abelian Stokes
formula. We study also the invariance properties of the (trace of the) holonomy
under suitable transformation groups acting on the pairs (A,B).
In this way we are able to define observables for both topological and
non-topological quantum field theories of the BF type. In the non topological
case, the surface terms may be relevant for the understanding of the
quark-confinement problem. In the topological case the (perturbative)
four-dimensional quantum BF-theory is expected to yield invariants of imbedded
(or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page
Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes
We present a numerical study of turbulence and dynamo action in stratified
shearing boxes with zero magnetic flux. We assume that the fluid obeys the
perfect gas law and has finite (constant) thermal diffusivity. We choose
radiative boundary conditions at the vertical boundaries in which the heat flux
is propor- tional to the fourth power of the temperature. We compare the
results with the corresponding cases in which fixed temperature boundary
conditions are applied. The most notable result is that the formation of a
fully convective state in which the density is nearly constant as a function of
height and the heat is transported to the upper and lower boundaries by
overturning motions is robust and persists even in cases with radiative
boundary conditions. Interestingly, in the convective regime, although the
diffusive transport is negligible the mean stratification does not relax to an
adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter
Magnetic Helicities and Dynamo Action in Magneto-rotationally Driven Turbulence
We examine the relationship between magnetic flux generation, taken as an
indicator of large-scale dynamo action, and magnetic helicity, computed as an
integral over the dynamo volume, in a simple dynamo. We consider dynamo action
driven by Magneto-Rotational Turbulence (MRT) within the shearing-box
approximation. We consider magnetically open boundary conditions that allow a
flux of helicity in or out of the computational domain. We circumvent the
problem of the lack of gauge invariance in open domains by choosing a
particular gauge -- the winding gauge -- that provides a natural interpretation
in terms of average winding number of pairwise field lines. We use this gauge
precisely to define and measure the helicity and helicity flux for several
realizations of dynamo action. We find in these cases, that the system as a
whole does not break reflectional symmetry and the total helicity remains small
even in cases when substantial magnetic flux is generated. We find no
particular connection between the generation of magnetic flux and the helicity
or the helicity flux through the boundaries. We suggest that this result may be
due to the essentially nonlinear nature of the dynamo processes in MRT.Comment: 26 pages, 10 figures, ApJ accepte
Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
General boundary conditions ("branes") for the Poisson sigma model are
studied. They turn out to be labeled by coisotropic submanifolds of the given
Poisson manifold. The role played by these boundary conditions both at the
classical and at the perturbative quantum level is discussed. It turns out to
be related at the classical level to the category of Poisson manifolds with
dual pairs as morphisms and at the perturbative quantum level to the category
of associative algebras (deforming algebras of functions on Poisson manifolds)
with bimodules as morphisms. Possibly singular Poisson manifolds arising from
reduction enter naturally into the picture and, in particular, the construction
yields (under certain assumptions) their deformation quantization.Comment: 21 pages, 2 figures; minor corrections, references updated; final
versio
AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz-
Zaboronsky superfield formalism using the language of graded manifolds. As a
main illustarting example, to every Courant algebroid structure we associate
canonically a three-dimensional topological sigma-model. Using the AKSZ
formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon
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