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

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.