Spinorial higher-spin gauge theory from IKKT model in Euclidean and Minkowski signatures

Abstract

Abstract We explore the semi-classical relation between the fuzzy 4-hyperboloid H N 4 $$ {H}_N^4 $$ and non-compact quantized twistor space ℙ N 1 , 2 $$ {\mathbb{P}}_N^{1,2} $$ at large N. This provides two backgrounds of the IKKT matrix model via two natural stereographic projections, leading to higher-spin gauge theories with Euclidean and Minkowski signature denoted by HS-IKKT. The resulting higher-spin gauge theory can be understood as an uplift of N $$ \mathcal{N} $$ = 4 super Yang-Mills to twistor space. The action of HS-IKKT is written using a spinor formalism in both in Euclidean and Minkowski signature. We then compute the tree-level amplitudes of the massless sector within the Yang-Mills part of the HS-IKKT model in the flat limit in Euclidean signature. All n-point tree-level scattering amplitudes for n ≥ 4 of this sector are found to vanish in the flat limit.

Keywords

• Higher Spin Gravity
• Matrix Models
• Non-Commutative Geometry