One-loop corrections to the spectral action

Teun Nuland (Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, Nijmegen, AJ, 525, The Netherlands) ; Walter Suijlekom (Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, Nijmegen, AJ, 525, The Netherlands)

We analyze the perturbative quantization of the spectral action in noncommutative geometry and establish its one-loop renormalizability in a generalized sense, while staying within the spectral framework of noncommutative geometry. Our result is based on the perturbative expansion of the spectral action in terms of higher Yang-Mills and Chern-Simons forms. In the spirit of random noncommutative geometries, we consider the path integral over matrix fluctuations around a fixed noncommutative gauge background and show that the corresponding one-loop counterterms are of the same form so that they can be safely subtracted from the spectral action. A crucial role will be played by the appropriate Ward identities, allowing for a fully spectral formulation of the quantum theory at one loop.

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Published on:
12 May 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 5
Pages 1-15
DOI:
https://doi.org/10.1007/JHEP05(2022)078
arXiv:
2107.08485
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: