Scaling limits of the fuzzy sphere at one loop

By C. Chu, J. Madore, H. Steinacker. 2001

138 citations recorded by the source corpus.

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 2? 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''.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8ceab116eb2494763a9829c8dea83b24fc665220

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In Mathematical Physics

1. H. Steinacker
2. B. Jurčo
3. J. Wess
4. P. Schupp
5. R. Szabo
6. S. J. Tongeren

In Nuclear and High Energy Physics

1. H. Steinacker
2. B. Jurčo
3. J. Wess
4. P. Schupp
5. R. Szabo
6. S. J. Tongeren

In Statistical and Nonlinear Physics

1. H. Steinacker
2. B. Jurčo
3. P. Schupp
4. J. Wess
5. R. Szabo
6. S. J. Tongeren

Citations in the corpus

• The standard model on non-commutative space-time (2001, methodology): “Note that the ultra-violet and infra-red mixing is absent in the case of Φ(4)-theory on a fuzzy sphere [27], where the quantization has been performed via path integrals.”
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model (2003, background): “ because there are only finitely many degrees of freedom. However, this does not necessarily make them easy to evaluate: e.g. for scalar fields, one is forced to resort to perturbation theory (see e.g. [34]), which is even more complicated than in the classical case. The main advantage of our matrix f”