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arXiv · 2512.03161

A New Type of Saddle in the Euclidean IKKT Matrix Model and Its Emergent Geometry

Henry Liao·Reishi Maeta
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Abstract

We study the equation of motion of the Euclidean IKKT matrix model, and realize a new type of classical saddle that only exists in $N\rightarrow\infty$ limit. Under the assumption that the matrices are the generators of $\mathfrak{so}(n,m)$, we identify a unique solution, that is, $\mathfrak{so}(1,3)$. Even though it has $6$ generators and thus $6$ non-zero matrices, they are not independent due to the $2$ Casimir constraints in $\mathfrak{so}(1,3)$. 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 $\mathrm{SU}(2)$ isometry, which is closely related to the Taub NUT/Bolt geometry and, more broadly, to black hole physics.

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Henry Liao, Reishi Maeta. 2025-12-02. A New Type of Saddle in the Euclidean IKKT Matrix Model and Its Emergent Geometry. https://arxiv.org/abs/2512.03161

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