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arXiv · 2405.09804

Quantum $\mathfrak{hs}$-Yang-Mills from the IKKT matrix model

Harold C. Steinacker·Tung Tran
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Abstract

We study the one-loop effective action of the higher-spin gauge theory induced by the IKKT matrix model on a $\mathcal{M}^{1,3}\times \mathcal{K}$ background, where $\mathcal{M}^{1,3}$ is an FLRW cosmological spacetime brane and $\mathcal{K}$ are compact fuzzy extra dimensions. In particular, we show that all non-abelian ($\mathfrak{hs}$-valued) gauge fields in this model acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a massive non-abelian quantum $\mathfrak{hs}$-Yang-Mills theory, whose detailed structure depends on $\mathcal{K}$. The stabilization of $\mathcal{K}$ at one loop is understood as a result of the coupling between $\mathcal{K}$ and the $U(1)$-flux bundle on space-time. This flux stabilization induces the KK scale into the $\mathcal{N} = 4$ SYM sector of the model, which break superconformal symmetry.

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Harold C. Steinacker, Tung Tran. 2024-05-16. Quantum $\mathfrak{hs}$-Yang-Mills from the IKKT matrix model. https://arxiv.org/abs/2405.09804

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