A twistorial description of the IKKT-matrix model

We consider the fuzzy 4-sphere S_N^4 as a background in the IKKT matrix model, and explore the relation between S_N^4 and fuzzy twistor space in the semi-classical limit. A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of 𝒩 = 4 super-symmetric Yang-Mills (SYM) in 4 d . On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of 𝒩 = 4 SYM, with vertices that have more than two derivatives. We obtain its (Euclidean) spacetime action using the Penrose transform. Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in 4 d flat space obtained in [ 1 , 2 ]. The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. The self-dual gauge sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a ℬℱ -type action on commutative deformed projective twistor space.