Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model

We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make the fuzzy sphere as a classical solution of the model. Majorana mass term is also added to make it supersymmetric. We consider two large $N$ limits, one corresponding to a gauge theory on a commutative sphere and the other to that on a noncommutative plane. We also investigate stability of the fuzzy sphere by calculating one-loop effective action around classical solutions. In the final part of this paper, we consider another matrix model which gives a supersymmetric gauge theory on the fuzzy sphere. In this matrix model, only Chern-Simons term is added and supersymmetry transformation is modified.Comment: 31 pages, more investigations of the theory in the commutative limit and references adde

Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions

We consider a U(2) Yang-Mills theory on M x S_F^2 where M is an arbitrary noncommutative manifold and S_F^2 is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in arXiv:0905.2338, we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane and find that, in certain limits, it admits noncommutative, non-BPS vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.Comment: 18+1 pages, typos corrected, published versio

On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry

Scalar field theories with quartic interaction are quantized on fuzzy $S^2$ and fuzzy $S^2\times S^2$ to obtain the 2- and 4-point correlation functions at one-loop. Different continuum limits of these noncommutative matrix spheres are then taken to recover the quantum noncommutative field theories on the noncommutative planes ${\mathbb R}^2$ and ${\mathbb R}^4$ respectively. The canonical limit of large stereographic projection leads to the usual theory on the noncommutative plane with the well-known singular UV-IR mixing. A new planar limit of the fuzzy sphere is defined in which the noncommutativity parameter ${\theta}$, beside acting as a short distance cut-off, acts also as a conventional cut-off ${\Lambda}=\frac{2}{\theta}$ in the momentum space. This noncommutative theory is characterized by absence of UV-IR mixing. The new scaling is implemented through the use of an intermediate scale that demarcates the boundary between commutative and noncommutative regimes of the scalar theory. We also comment on the continuum limit of the $4-$point function.Comment: Latex File, 3 Figure

Optimal Iris Fuzzy Sketches

Fuzzy sketches, introduced as a link between biometry and cryptography, are a way of handling biometric data matching as an error correction issue. We focus here on iris biometrics and look for the best error-correcting code in that respect. We show that two-dimensional iterative min-sum decoding leads to results near the theoretical limits. In particular, we experiment our techniques on the Iris Challenge Evaluation (ICE) database and validate our findings.Comment: 9 pages. Submitted to the IEEE Conference on Biometrics: Theory, Applications and Systems, 2007 Washington D

The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory

We consider different large ${\cal N}$ limits of the one-dimensional Chern-Simons action i\int dt~ \Tr (\del_0 +A_0) where $A_0$ is an ${\cal N}\times{\cal N}$ antihermitian matrix. The Hilbert space on which $A_0$ acts as a linear transformation is taken as the quantization of a $2k$-dimensional phase space ${\cal M}$ with different gauge field backgrounds. For slowly varying fields, the large ${\cal N}$ limit of the one-dimensional CS action is equal to the $(2k+1)$-dimensional CS theory on ${\cal M}\times {\bf R}$. Different large ${\cal N}$ limits are parametrized by the gauge fields and the dimension $2k$. The result is related to the bulk action for quantum Hall droplets in higher dimensions. Since the isometries of ${\cal M}$ are gauged, this has implications for gravity on fuzzy spaces. This is also briefly discussed.Comment: 37 pages, references and a comment adde