A twistorial description of the IKKT-matrix model

[en] We consider the fuzzy 4-sphere SN4 as a background in the IKKT matrix model, and explore the relation between SN4 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 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 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 BF-type action on commutative deformed projective twistor space.

Research center :

AGIF - Algèbre, Géométrie et Interactions fondamentales

Disciplines :

Physics

Author, co-author :

Steinacker, Harold C. ^✱; Department of Physics, University of Vienna, Vienna, Austria

Tran, Vuong ; Université de Mons - UMONS > Faculté des Sciences > Service de Physique de l'Univers, Champs et Gravitation

^✱ These authors have contributed equally to this work.

Language :

English

Title :

A twistorial description of the IKKT-matrix model

Publication date :

25 November 2022

Journal title :

Journal of High Energy Physics

ISSN :

1126-6708

eISSN :

1029-8479

Publisher :

Springer Science and Business Media Deutschland GmbH

Volume :

2022

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.springer.com/content/pdf/10.1007/JHEP11(2022)146.pdf

Research unit :

S827 - Physique de l'Univers, Champs et Gravitation

Research institute :

R150 - Institut de Recherche sur les Systèmes Complexes

Funders :

ERC - European Research Council [BE]
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Funding text :

This work is partially supported by the Fonds de la Recherche Scientifique un- der Grants No. F.4503.20 (HighSpinSymm), Grant No. 40003607 (HigherSpinGraWave), T.0022.19 (Fundamental issues in extended gravitational theories) and the funding from the European Research Council (ERC) under Grant No. 101002551.

Data Set :

A twistorial description of the IKKT-matrix model

Commentary :

54 pages, references added, published version

Available on ORBi UMONS :

since 25 December 2022

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