9,169 research outputs found
Cohomological Yang-Mills Theory in Eight Dimensions
We construct nearly topological Yang-Mills theories on eight dimensional
manifolds with a special holonomy group. These manifolds are the Joyce manifold
with holonomy and the Calabi-Yau manifold with SU(4) holonomy. An
invariant closed four form on the manifold allows us to
define an analogue of the instanton equation, which serves as a topological
gauge fixing condition in BRST formalism. The model on the Joyce manifold is
related to the eight dimensional supersymmetric Yang-Mills theory. Topological
dimensional reduction to four dimensions gives non-abelian Seiberg-Witten
equation.Comment: 9 pages, latex, Talk given at APCTP Winter School on Dualities in
String Theory, (Sokcho, Korea), February 24-28, 199
Special Quantum Field Theories In Eight And Other Dimensions
We build nearly topological quantum field theories in various dimensions. We
give special attention to the case of 8 dimensions for which we first consider
theories depending only on Yang-Mills fields. Two classes of gauge functions
exist which correspond to the choices of two different holonomy groups in
SO(8), namely SU(4) and Spin(7). The choice of SU(4) gives a quantum field
theory for a Calabi-Yau fourfold. The expectation values for the observables
are formally holomorphic Donaldson invariants. The choice of Spin(7) defines
another eight dimensional theory for a Joyce manifold which could be of
relevance in M- and F-theories. Relations to the eight dimensional
supersymmetric Yang-Mills theory are presented. Then, by dimensional reduction,
we obtain other theories, in particular a four dimensional one whose gauge
conditions are identical to the non-abelian Seiberg-Witten equations. The
latter are thus related to pure Yang-Mills self-duality equations in 8
dimensions as well as to the N=1, D=10 super Yang-Mills theory. We also exhibit
a theory that couples 3-form gauge fields to the second Chern class in eight
dimensions, and interesting theories in other dimensions.Comment: 36 pages, latex. References have been added together with a not
Superlubricity - a new perspective on an established paradigm
Superlubricity is a frictionless tribological state sometimes occurring in
nanoscale material junctions. It is often associated with incommensurate
surface lattice structures appearing at the interface. Here, by using the
recently introduced registry index concept which quantifies the registry
mismatch in layered materials, we prove the existence of a direct relation
between interlayer commensurability and wearless friction in layered materials.
We show that our simple and intuitive model is able to capture, down to fine
details, the experimentally measured frictional behavior of a hexagonal
graphene flake sliding on-top of the surface of graphite. We further predict
that superlubricity is expected to occur in hexagonal boron nitride as well
with tribological characteristics very similar to those observed for the
graphitic system. The success of our method in predicting experimental results
along with its exceptional computational efficiency opens the way for modeling
large-scale material interfaces way beyond the reach of standard simulation
techniques.Comment: 18 pages, 7 figure
Inverse moment problem for elementary co-adjoint orbits
We give a solution to the inverse moment problem for a certain class of
Hessenberg and symmetric matrices related to integrable lattices of Toda type.Comment: 13 page
Magnetic friction due to vortex fluctuation
We use Monte Carlo and molecular dynamics simulation to study a magnetic
tip-sample interaction. Our interest is to understand the mechanism of heat
dissipation when the forces involved in the system are magnetic in essence. We
consider a magnetic crystalline substrate composed of several layers
interacting magnetically with a tip. The set is put thermally in equilibrium at
temperature T by using a numerical Monte Carlo technique. By using that
configuration we study its dynamical evolution by integrating numerically the
equations of motion. Our results suggests that the heat dissipation in this
system is closed related to the appearing of vortices in the sample.Comment: 6 pages, 41 figure
Theory of friction: contribution from fluctuating electromagnetic field
We calculate the friction force between two semi-infinite solids in relative
parallel motion (velocity ), and separated by a vacuum gap of width . The
friction force result from coupling via a fluctuating electromagnetic field,
and can be considered as the dissipative part of the van der Waals interaction.
We consider the dependence of the friction force on the temperature , and
present a detailed discussion of the limiting cases of small and large and
.Comment: 15 pages, No figure
Scalar Representation and Conjugation of Set-Valued Functions
To a function with values in the power set of a pre-ordered, separated
locally convex space a family of scalarizations is given which completely
characterizes the original function. A concept of a Legendre-Fenchel conjugate
for set-valued functions is introduced and identified with the conjugates of
the scalarizations. Using this conjugate, weak and strong duality results are
proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435
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