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Correction to: Ann. Henri Poincaré https://doi.org/10.1007/s00023-021-01138-w
Three equations in the body of Theorem 6.1 of [1] (present in the author’s submission) did not appear in the published article due to a mistake by the Author Corrections Team of Springer Nature Journals Production. In that theorem, the spectral action \(\frac{1}{4}{{\,\textrm{Tr}\,}}_\mathcal {H}g(D)\) for polynomial g is computed in terms of several sectors. However, in the published version, only one of such, namely
appears defined. The correct group of equations (6.2), as the author submitted them, should have been displayed as:
(Secondarily: In the proof, the polynomial appearing in this errata in the spectral action \(\frac{1}{4}{{\,\textrm{Tr}\,}}_\mathcal {H}g(D)\) was called f there; here, we use g in order not to give the impression that the ‘f’ in \( S_{\textsc {ym}}^\textrm{f},\ldots ,S^\textrm{f}_\vartheta \) refers to the polynomial; straight ‘f’ rather means ‘fuzzy space’. The enormous flexibility of arXiv regarding the font choices takes care of this distinction; hence the polynomial in question is uniformly called f in the preprint version which is, and already before this errata was, correct.)
Reference
Pérez-Sánchez, Carlos I.: On multimatrix models motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model. Ann. Henri Poincaré, 23, 1979–2023 arXiv:2105.01025
Acknowledgements
The author is thankful to Makoto Yamashita for pointing out at the missing lines. This work was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No818066) and also by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2181/1-390900948 (the Heidelberg STRUCTURES Cluster of Excellence).
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Communicated by Claude-Alain Pillet.
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Perez-Sanchez, C.I. Correction to: ‘On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model’. Ann. Henri Poincaré (2024). https://doi.org/10.1007/s00023-024-01456-9
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DOI: https://doi.org/10.1007/s00023-024-01456-9