Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-05-22
Nucl.Phys. B671 (2003) 401-431
Physics
High Energy Physics
High Energy Physics - Theory
Latex File, 3 Figures
Scientific paper
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.
Vaidya Sachindeo
Ydri Badis
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