One-loop Effects on the Fuzzy Sphere

  • Harold Steinacker
ITP - Hörsaal 1 Universität Leipzig, ITP (Leipzig)


The two-point function for scalar field theory on the fuzzy sphere is calculated at one loop, including planar and nonplanar contributions. It turns out that there is no UV/IR mixing on the fuzzy sphere. The limit of the commutative sphere 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 appears. This provides an explanation of the UV/IR mixing as an infinite variant of the ``noncommutative anomaly''.

25.09.01 29.09.01

Noncommutative Geometry, Strings and Renormalization

Universität Leipzig, ITP ITP - Hörsaal 1

H. Grosse

G. Rudolph

Klaus Sibold

Julius Wess

Eberhard Zeidler