47 research outputs found
Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
We find using Monte Carlo simulation the phase structure of noncommutative U(1) gauge theory in two dimensions with the fuzzy sphere S^2_N as a non-perturbative regulator. There are three phases of the model. i) A matrix phase where the theory is essentially SU(N) Yang-Mills reduced to zero dimension . ii) A weak coupling fuzzy sphere phase with constant specific heat and iii) A strong coupling fuzzy sphere phase with non-constant specific heat. The order prameter distinguishing the matrix phase from the sphere phase is the radius of the fuzzy sphere. The three phases meet at a triple point. We also give the theoretical one-loop and 1/N expansion predictions for the transition lines which are in good agreement with the numerical data. A Monte Carlo measurement of the triple point is also given
New Scaling Limit for Fuzzy Spheres
Using a new scaling limit as well as a new cut-off procedure, we show that
theory on noncommutative can be obtained from the
corresponding theory on fuzzy . The star-product on
this noncommutative is effectively local in the sense that the
theory naturally has an ultra-violet cut-off which is inversely
proportional to the noncommutativity , i.e . We show that the UV-IR mixing in this case is absent to one
loop in the point function and also comment on the point function.Comment: 13 pages, late
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
Non-Linear Sigma Model on the Fuzzy Supersphere
In this note we develop fuzzy versions of the supersymmetric non-linear sigma
model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been
used to obtain the fuzzy CP^1 model. Our approach utilizes the use of
supersymmetric extensions of these projectors. Here we obtain these (super)
-projectors and quantize them in a fashion similar to the one given in
hep-th/0212133. We discuss the interpretation of the resulting model as a
finite dimensional matrix model.Comment: 11 pages, LaTeX, corrected typo
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