A twistorial description of the IKKT-matrix model

• Published in: The journal of high energy physics Vol. 2022; no. 11; pp. 146 - 51
• Main Authors: Steinacker, Harold C., Tran, Tung
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 25.11.2022; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Apexes; Classical and Quantum Gravitation; Elementary Particles; Gauge theory; Gravitation theory; Gravity; High energy physics; Higher Spin Gravity; Matrix Models; Non-Commutative Geometry; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spacetime; String Theory; Symmetry; Higher Spin Gravity; Non-Commutative Geometry; Matrix Models
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2022)146

A bstract 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.