33 research outputs found
Monopoles and Solitons in Fuzzy Physics
Monopoles and solitons have important topological aspects like quantized
fluxes, winding numbers and curved target spaces. Naive discretizations which
substitute a lattice of points for the underlying manifolds are incapable of
retaining these features in a precise way. We study these problems of discrete
physics and matrix models and discuss mathematically coherent discretizations
of monopoles and solitons using fuzzy physics and noncommutative geometry. A
fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov
bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one
Author corrected. To appear in Commun.Math.Phy
The Fermion Doubling Problem and Noncommutative Geometry
We propose a resolution for the fermion doubling problem in discrete field
theories based on the fuzzy sphere and its Cartesian products.Comment: 12 pages Latex2e, no figures, typo
Towards Noncommutative Fuzzy QED
We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4.
We write down the effective action on fuzzy S**2 x S**2 and show the existence
of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We
also give a derivation of the beta function and comment on the limit of large
mass of the normal scalar fields. We also discuss topology change in this 4
fuzzy dimensions arising from the interaction of fields (matrices) with
spacetime through its noncommutativity.Comment: 33 page
On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories
Invariant (nonplanar) anomaly of noncommutative QED is reexamined. It is
found that just as in ordinary gauge theory UV regularization is needed to
discover anomalies, in noncommutative case, in addition, an IR regularization
is also required to exhibit existence of invariant anomaly. Thus resolving the
controversy in the value of invariant anomaly, an expression for the
unintergrated anomaly is found. Schwinger terms of the current algebra of the
theory are derived.Comment: LaTeX, axodraw.sty, 1 figure; v2: Typos corrected, References added,
Version to appear in Int. J. Mod. Phys. A (2006
Quantum effective potential for U(1) fields on S^2_L X S^2_L
We compute the one-loop effective potential for noncommutative U(1) gauge
fields on S^2_L X S^2_L. We show the existence of a novel phase transition in
the model from the 4-dimensional space S^2_L X S^2_L to a matrix phase where
the spheres collapse under the effect of quantum fluctuations. It is also shown
that the transition to the matrix phase occurs at infinite value of the gauge
coupling constant when the mass of the two normal components of the gauge field
on S^2_L X S^2_L is sent to infinity.Comment: 13 pages. one figur
Dynamical generation of a nontrivial index on the fuzzy 2-sphere
In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP)
monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and
showed that it has a nonzero topological charge in the formalism based on the
Ginsparg-Wilson relation. In this paper, by showing that the TP monopole
configuration is stabler than the U(2) gauge theory without any condensation in
the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for
dynamical generation of a nontrivial index. We further analyze the instability
and decay processes of the U(2) gauge theory and the TP monopole configuration.Comment: Latex2e, 30 pages, 4 figures, the topological charge for a monopole
configuration is corrected, reference added, the final version to appear in
Physical Review D (the typos mentioned in the erratum are corrected
Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator
It is shown that the local axial anomaly in dimensions emerges naturally
if one postulates an underlying noncommutative fuzzy structure of spacetime .
In particular the Dirac-Ginsparg-Wilson relation on is shown to
contain an edge effect which corresponds precisely to the ``fuzzy''
axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant
expansion of the quark propagator in the form where
is the lattice spacing on , is
the covariant noncommutative chirality and is an effective
Dirac operator which has essentially the same IR spectrum as
but differes from it on the UV modes. Most remarkably is the fact that both
operators share the same limit and thus the above covariant expansion is not
available in the continuum theory . The first bit in this expansion
although it vanishes as it stands in the continuum
limit, its contribution to the anomaly is exactly the canonical theta term. The
contribution of the propagator is on the other hand
equal to the toplogical Chern-Simons action which in two dimensions vanishes
identically .Comment: 26 pages, latex fil