7,833 research outputs found
Spectral geometry with a cut-off: topological and metric aspects
Inspired by regularization in quantum field theory, we study topological and
metric properties of spaces in which a cut-off is introduced. We work in the
framework of noncommutative geometry, and focus on Connes distance associated
to a spectral triple (A, H, D). A high momentum (short distance) cut-off is
implemented by the action of a projection P on the Dirac operator D and/or on
the algebra A. This action induces two new distances. We individuate conditions
making them equivalent to the original distance. We also study the
Gromov-Hausdorff limit of the set of truncated states, first for compact
quantum metric spaces in the sense of Rieffel, then for arbitrary spectral
triples. To this aim, we introduce a notion of "state with finite moment of
order 1" for noncommutative algebras. We then focus on the commutative case,
and show that the cut-off induces a minimal length between points, which is
infinite if P has finite rank. When P is a spectral projection of , we work
out an approximation of points by non-pure states that are at finite distance
from each other. On the circle, such approximations are given by Fejer
probability distributions. Finally we apply the results to Moyal plane and the
fuzzy sphere, obtained as Berezin quantization of the plane and the sphere
respectively.Comment: Reference added. Minor corrections. Published version. 38 pages, 2
figures. Journal of Geometry and Physics 201
ABJM Baryon Stability and Myers effect
We consider magnetically charged baryon vertex like configurations in AdS^4 X
CP^3 with a reduced number of quarks l. We show that these configurations are
solutions to the classical equations of motion and are stable beyond a critical
value of l. Given that the magnetic flux dissolves D0-brane charge it is
possible to give a microscopical description in terms of D0-branes expanding
into fuzzy CP^n spaces by Myers dielectric effect. Using this description we
are able to explore the region of finite 't Hooft coupling.Comment: 29 pages, Latex; minor changes; version to appear in JHE
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