Braided symmetries in noncommutative field theory

Grigorios Giotopoulos*, Richard J. Szabo

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

8 Citations (Scopus)
26 Downloads (Pure)


We give a pedagogical introduction to L ∞-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective field theories in string theory. We review recent developments which formulate field theories with braided gauge symmetries as a new means of overcoming several obstacles in the standard noncommutative theories, such as the restrictions on gauge algebras and matter fields. These theories can be constructed by using techniques from Drinfel'd twist deformation theory, which we review in some detail, and their symmetries and dynamics are controlled by a new homotopy algebraic structure called a 'braided L ∞-algebra'. We expand and elaborate on several novel theoretical issues surrounding these constructions, and present three new explicit examples: the standard noncommutative scalar field theory (regarded as a braided field theory), a braided version of BF theory in arbitrary dimensions (regarded as a higher gauge theory), and a new braided version of noncommutative Yang-Mills theory for arbitrary gauge algebras.

Original languageEnglish
Article number353001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number35
Early online date9 Aug 2022
Publication statusPublished - 2 Sept 2022


  • Drinfel'd twists
  • Homotopy algebras
  • Noncommutative field theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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