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New type of saddle in the Euclidean IKKT matrix model and its emergent geometry

Henry Liao1,* and Reishi Maeta1,2,3,†

  • *Contact author: henryliao.physics@gmail.com
  • †Contact author: maeta-reishi@hiroshima-u.ac.jp
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Phys. Rev. D 114, 026021 – Published 16 July, 2026

DOI: https://doi.org/10.1103/gfcj-9vb3

Abstract

We study the equation of motion of the Euclidean Ishibashi-Kawai-Kitazawa-Tsuchiya matrix model, and realize a new type of classical saddle that only exists in the N→∞ limit. Under the assumption that the matrices are the generators of so(n,m), we identify a unique solution, that is, so(1,3). Even though it has 6 generators and thus 6 nonzero matrices, they are not independent due to the 2 Casimir constraints in so(1,3). Exploiting the Lie-algebraic structure and the Casimir constraints, we derive a four-dimensional space that a test scalar propagates on. The associated metric possesses SU(2) isometry, which is closely related to the Taub–Newman-Unti-Tamburino/Bolt geometry and may, more broadly, be related to black hole physics.

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Outline

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Phys. Rev. D 114, 026021– Published 16 July, 2026
  • Received 29 December 2025
  • Accepted 25 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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