Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity

Abstract

We define a new homotopy algebraic structure, that we call a braided $L_{\infty }$-algebra, and use it to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act on the solutions of the field equations. We use Drinfel'd twist deformation quantization techniques to generate new noncommutative deformations of classical field theories with braided gauge symmetries, which we compare to the more conventional theories with star-gauge symmetries. We apply our formalism to introduce a braided version of general relativity without matter fields in the Einstein-Cartan-Palatini formalism. In the limit of vanishing deformation parameter, the braided theory of noncommutative gravity reduces to classical gravity without any extensions.

68 pages; v2: presentation improved, references added; Final version to be published in Letters in Mathematical Physics

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Cited by in corpus (9)

• Braided Symmetries in Noncommutative Field Theory
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Non-commutative gauge symmetry from strong homotopy algebras
• T-Minkowski noncommutative spacetimes II: classical field theory
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Generalized symmetries as homotopy Lie algebras
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• Noncommutative dyonic black holes sourced by nonlinear electromagnetic fields