Work

Non-associative algebras of cubic matrices and their gauge theories

Year: 2025

Type: article

Abstract: A bstract Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated L ∞ algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep09(2025)003

Authors: Ralph Blumenhagen, Antonia Paraskevopoulou, Thomas Raml

Institutions: Max Planck Institute for Physics, Ludwig-Maximilians-Universität München

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: G1897041155, G4066435496, EXC 2094: ORIGINS: Vom Ursprung des Universums bis zu den ersten Bausteinen des Lebens