8 research outputs found
Intersecting Quantum Gravity with Noncommutative Geometry - a Review
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section
On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
We investigate some issues that are relevant for the derivation of
experimental limits on the parameters of canonical noncommutative spacetimes.
By analyzing a simple Wess-Zumino-type model in canonical noncommutative
spacetime with soft supersymmetry breaking we explore the implications of
ultraviolet supersymmetry on low-energy phenomenology. The fact that new
physics in the ultraviolet can modify low-energy predictions affects
significantly the derivation of limits on the noncommutativity parameters based
on low-energy data. These are, in an appropriate sense here discussed,
``conditional limits''. We also find that some standard techniques for an
effective low-energy description of theories with non-locality at short
distance scales are only applicable in a regime where theories in canonical
noncommutative spacetime lack any predictivity, because of the strong
sensitivity to unknown UV physics. It appears useful to combine high-energy
data, from astrophysics, with the more readily available low-energy data.Comment: 14 page
Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
Fuzzy spheres appear as classical solutions in a matrix model obtained via
dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons
term. Well-defined perturbative expansion around these solutions can be
formulated even for finite matrix size, and in the case of coincident fuzzy
spheres it gives rise to a regularized U() gauge theory on a noncommutative
geometry. Here we study the matrix model nonperturbatively by Monte Carlo
simulation. The system undergoes a first order phase transition as we change
the coefficient () of the Chern-Simons term. In the small
phase, the large properties of the system are qualitatively the same as in
the pure Yang-Mills model (), whereas in the large phase a
single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are
observed as meta-stable states, and we argue in particular that the
coincident fuzzy spheres cannot be realized as the true vacuum in this model
even in the large limit. We also perform one-loop calculations of various
observables for arbitrary including . Comparison with our Monte Carlo
data suggests that higher order corrections are suppressed in the large
limit.Comment: Latex 37 pages, 13 figures, discussion on instabilities refined,
references added, typo corrected, the final version to appear in JHE
The role of the Seiberg–Witten field redefinition in renormalization of noncommutative chiral electrodynamics
It has been conjectured in the literature that renormalizability of the
-expanded noncommutative gauge theories improves when one takes into
account full nonuniqueness of the Seiberg-Witten expansion, which relates
noncommutative (`high-energy') with commutative (`low-energy') fields. In order
to check this conjecture we analyze renormalizability of the noncommutative
chiral electrodynamics: we quantize the action which contains all possible
terms implied by the SW map. After renormalization we arrive at a different
theory in which the relation between the coupling constants is changed. This
means that the -expanded chiral electrodynamics is not renormalizable:
when fermions are included, the SW expansion is not preserved in quantization.Comment: 16 page