Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry

Vladislav G. Kupriyanov*, Richard J. Szabo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
11 Downloads (Pure)


We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a P ∞-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an L ∞-algebra which is not a P ∞-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a P ∞-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on A ∞-algebras.

Original languageEnglish
Article number035201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number3
Early online date28 Dec 2021
Publication statusPublished - 21 Jan 2022


  • deformation quantization
  • gauge symmetry
  • homotopy algebras
  • noncommutative geometry

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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