Gauge Theories on the Noncommutative Sphere

Abstract

Gauge theories are formulated on the noncommutative two-sphere. These theories have only finite number of degrees of freedom, nevertheless they exhibit both the gauge symmetry and the SU(2) "Poincaré" symmetry of the sphere. In particular, the coupling of gauge fields to chiral fermions is naturally achieved. 1 However, see a recent progress in understanding substringy scales via D-branes [1].

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

“…On the other hand, a fuzzy space description for gauge theory was studied in some papers, including [65,66,67,68,69,70,71,72,73,74,75,76,58].…”

Fractional quantum Hall effect on the two-sphere: A matrix model proposal

“…The matrix model describing this situation is expected to reproduce features of the "fuzzy sphere", at least for the fully filled case. (For early work on fuzzy spheres and some further discussions see [18][19][20][21][22][23][24]. )…”

A Nonperturbative Regularization of the Supersymmetric Schwinger Model

“…It was actually from the nocommutative rather than from the supersymmetric side where the motivation for this work came from. One could witness in the last few years a lot of activity [4,5,6,7,8,9,10,11] concerning model building on the so-called fuzzy sphere. The latter concept was probably invented by Berezin [12], but the idea to use it for regularization of scalar field theories was independently advocated firstly in [13] and [14].…”