Spinorial description for Lorentzian $\mathfrak{hs}$-IKKT

Abstract

We introduce a novel spinorial description for the higher-spin gauge theory induced by the IKKT matrix model on an FLRW spacetime with Lorentzian signature, called Lorentzian $\mathfrak{hs}$-IKKT theory. The new description is based on Weyl spinors transforming under the space-like isometry subgroup $SL(2,\mathbb{C})$ of the structure group $SO(2,4)\simeq SU(2,2)$. It allows us to exploit the full power of the spinor formalism in Lorentzian signature, in contrast to a previous formalism based on the compact subgroup $SU(2{)}_L\times SU(2{)}_R$ of $SU(2,2)$. Some cubic vertices of the Yang-Mills sector and the corresponding scattering amplitudes are computed. We observe that the $n$-point (for $n\ge 4$) tree-level amplitudes are typically non-trivial on-shell, but exponentially suppressed in the late-time regime. While Lorentz invariance of the higher-spin amplitudes is not manifest, it is expected to be restored by higher-spin gauge invariance.

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