424 research outputs found
T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences
This paper is the second part of a series of papers about a new notion of
T-homotopy of flows. It is proved that the old definition of T-homotopy
equivalence does not allow the identification of the directed segment with the
3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new
definition of T-homotopy equivalence is proposed, following the intuition of
refinement of observation. And it is proved that up to weak S-homotopy, a old
T-homotopy equivalence is a new T-homotopy equivalence. The left-properness of
the weak S-homotopy model category of flows is also established in this second
part. The latter fact is used several times in the next papers of this series.Comment: 20 pages, 3 figure
Deconfinement on for all gauge groups and duality to double Coulomb Gas
I study finite-temperature super Yang-Mills for any gauge
group , compactified from four
dimensions on a torus, . I examine
in particular the low temperature regime , where is the
length of the spatial circle with periodic boundary conditions and with
anti-periodic boundary conditions for the adjoint gauginos along the thermal
cycle . For small such we are in a regime were semiclassical
calculations can be performed and a transition occurs at much smaller
than . The transition is mediated by the competition between
non-perturbative objects including 'exotic' topological molecules: neutral and
magnetic bions composed of BPS and KK monopole constituents, with
different charges in the co-root lattice of the gauge group , and the
perturbative electrically charged W-bosons (along with their wino
superpartners). I determine a duality to a double Coulomb gas of neutral and
magnetic bions of different charges of their constituent monopole-instantons,
and W-bosons of both scalar and electric charges. Aharanov-Bohm interactions
exist between magnetic bions and W-bosons, and scalar charges of W-bosons and
neutral bions attract like charges, as opposed to the magnetic and electric
charges where like charges repel. It is hoped in the future that lattice
studies of this Coulomb gas can be done as in [1] for all gauge groups. It is
hoped that a dual lattice 'affine' XY model with symmetry breaking
perturbations can also be found in future studies of general gauge group as
done in [1] for .Comment: 40 pages, 0 figure
Crossed product extensions of spectral triples
Given a spectral triple and a -dynamical system where is dense in and is a locally compact
group, we extend the triple to a triplet
on the crossed product which can be promoted to a
modular-type twisted spectral triple within a general procedure exemplified by
two cases: the -algebra of the affine group and the conformal group acting
on a complete Riemannian spin manifold.Comment: Version 3: version to appear in Journal of Noncommutative Geometr
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