A twistorial description of the IKKT-matrix model

Abstract

Abstract We consider the fuzzy 4-sphere $$ {S}_N^4 $$ S N 4 as a background in the IKKT matrix model, and explore the relation between $$ {S}_N^4 $$ 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 $$ \mathcal{N} $$ N = 4 super-symmetric Yang-Mills (SYM) in 4d. 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 $$ \mathcal{N} $$ 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 4d 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 $$ \mathcal{BF} $$ BF -type action on commutative deformed projective twistor space.