2006/07/12 by Victor Gayral, V. Gayral, Bruno Iochum +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-007-0194-6
published as Commun.Math.Phys.273:415-443,2007
arxiv created 2006/07/12 · openalex publication_date 2007/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC ϕ4 theory on \T4, we show that this theory can be made renormalizable at least at one loop, and may be even beyond.