Abstract
AbstractWe define a new homotopy algebraic structure, that we call a braided $$L_\infty $$
L
∞
-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.
Funder
Serbian Ministry of Education, Science and Technological Development
Croatian Science Foundation Project
Engineering and Physical Sciences Research Council
Science and Technology Facilities Council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference56 articles.
1. Asakawa, T., Mori, M., Watamura, S.: Hopf algebra symmetry and string. Prog. Theor. Phys. 120, 659–689 (2008). arXiv:0805.2203 [hep-th]
2. Asakawa, T., Mori, M., Watamura, S.: Twist quantization of string and $$B$$-field background. JHEP 04, 117 (2009). arXiv:0811.1638 [hep-th]
3. Aschieri, P.: Cartan structure equations and Levi–Civita connection in braided geometry. arXiv:2006.02761 [math.QA]
4. Aschieri, P., Castellani, L.: Noncommutative $$D=4$$ gravity coupled to fermions. JHEP 06, 086 (2009). arXiv:0902.3817 [hep-th]
5. Aschieri, P., Castellani, L.: Noncommutative gravity solutions. J. Geom. Phys. 60, 375–393 (2010). arXiv:0906.2774 [hep-th]
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