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arXiv · 2510.27463

Boundary Integrability from the Fuzzy Three Sphere

Tamas Gombor·Adolfo Holguin
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Abstract

We consider $\mathfrak{so}_4$ invariant matrix product states (MPS) in the $\mathfrak{so}_6$ symmetric integrable spin chain and prove their integrability. These MPS appear as fuzzy three-sphere solutions of matrix models with Yang-Mills-type interactions, and in particular they correspond to scalar defect sectors of $N=4$ SYM. We find that the algebra formed by the fuzzy three-sphere generators naturally leads to a boundary reflection algebra and hence a solution to the boundary Yang-Baxter equation for every representation of the fuzzy three-sphere. This allows us to find closed formula for the overlaps of Bethe states of $\mathfrak{so}_6$ symmetric chains with the fuzzy three-sphere MPS for arbitrary bond dimensions.

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Tamas Gombor, Adolfo Holguin. 2025-10-31. Boundary Integrability from the Fuzzy Three Sphere. https://arxiv.org/abs/2510.27463

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