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PreprintCC BY 4.0arXiv

Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling

  • Harold C. Steinacker
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Abstract

This paper aims to clarify conceptual aspects of emergent structure in IKKT-type matrix models. Even without any adjustable parameters in the action, non-trivial matrix vacua do acquire a meaningful coupling constant, as well as two distinct uncertainty scales: a) the scale of noncommutativity of the matrix background, and b) the scale of quantum fluctuations of the matrices under the path integral. These scales are estimated for two prototypes of matrix backgrounds, known as Moyal-Weyl quantum plane and covariant quantum spacetime. Their relative importance separates two regimes: 1) the semi-classical regime interpreted in terms of semi-classical noncommutative geometry, and 2) the deep quantum regime usually interpreted in terms of holography. The quantum fluctuations around the background are shown to be negligible in the weak coupling regime. This justifies a basic assumption in previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.

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Cite

BibTeXRIS
BibTeX
@misc{steinacker2026quantum,
  title = {{Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling}},
  author = {Harold C. Steinacker},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.13294},
  eprint = {2605.13294},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.13294},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling
AU  - Harold C. Steinacker
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2605.13294
UR  - https://arxiv.org/abs/2605.13294
AB  - This paper aims to clarify conceptual aspects of emergent structure in IKKT-type matrix models. Even without any adjustable parameters in the action, non-trivial matrix vacua do acquire a meaningful coupling constant, as well as two distinct uncertainty scales: a) the scale of noncommutativity of the matrix background, and b) the scale of quantum fluctuations of the matrices under the path integral. These scales are estimated for two prototypes of matrix backgrounds, known as Moyal-Weyl quantum plane and covariant quantum spacetime. Their relative importance separates two regimes: 1) the semi-classical regime interpreted in terms of semi-classical noncommutative geometry, and 2) the deep quantum regime usually interpreted in terms of holography. The quantum fluctuations around the background are shown to be negligible in the weak coupling regime. This justifies a basic assumption in previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.
ER  -