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

TL;DR

This paper derives a massive non-abelian higher-spin Yang-Mills theory from the IKKT matrix model on a cosmological background with fuzzy extra dimensions, showing quantum effects induce mass and stabilize the extra dimensions.

Contribution

It demonstrates how quantum effects in the IKKT matrix model generate mass for higher-spin gauge fields and stabilize extra dimensions, leading to a massive non-abelian higher-spin Yang-Mills theory.

Findings

All non-abelian higher-spin gauge fields acquire mass via quantum effects.

Stabilization of fuzzy extra dimensions is achieved through flux coupling.

The model induces a KK scale that breaks superconformal symmetry.

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.