Scaling Limits of the Fuzzy Sphere at one Loop

Details Scaling Limits of the Fuzzy Sphere at one Loop Scaling Limits of the Fuzzy Sphere at one Loop

2001-06-22

arxiv.org/abs/hep-th/0106205v2

JHEP 0108 (2001) 038

Physics

High Energy Physics

High Energy Physics - Theory

16 pages. v2: add remarks on p.6, footnotes on p.6 and p.9 clarified in response to the referee suggestions for clearer presen

Scientific paper

10.1088/1126-6708/2001/08/038

We study the one loop dynamics of QFT on the fuzzy sphere and calculate the planar and nonplanar contributions to the two point function at one loop. We show that there is no UV/IR mixing on the fuzzy sphere. The fuzzy sphere is characterized by two moduli: a dimensionless parameter N and a dimensionful radius R. Different geometrical phases can obtained at different corners of the moduli space. In the limit of the commutative sphere, we find that the two point function is regular without UV/IR mixing; however quantization does not commute with the commutative limit, and a finite ``noncommutative anomaly'' survives in the commutative limit. In a different limit, the noncommutative plane R^2_theta is obtained, and the UV/IR mixing reappears. This provides an explanation of the UV/IR mixing as an infinite variant of the ``noncommutative anomaly''.

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