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