TY - JOUR

T1 - Braided L∞ -algebras, braided field theory and noncommutative gravity

AU - Dimitrijević Ćirić, Marija

AU - Giotopoulos, Grigorios

AU - Radovanović, Voja

AU - Szabo, Richard J.

N1 - Funding Information:
We thank Branislav Jurčo, Lukas Müller and Alexander Schenkel for helpful discussions and correspondence. The work of M.D.C. and V.R. is supported by Project ON171031 of the Serbian Ministry of Education, Science and Technological Development. The work of M.D.C. and R.J.S. was partially supported by the Croatian Science Foundation Project IP-2019-04-4168. The work of G.G. is supported by a Doctoral Training Grant from the UK Engineering and Physical Sciences Research Council. The work of R.J.S. was supported by the Consolidated Grant ST/P000363/1 from the UK Science and Technology Facilities Council.
Publisher Copyright:
© 2021, The Author(s).

PY - 2021/12

Y1 - 2021/12

N2 - We define a new homotopy algebraic structure, that we call a braided 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.

AB - We define a new homotopy algebraic structure, that we call a braided 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.

KW - Drinfeld twist

KW - L-algebra

KW - Noncommutative gravity

UR - http://www.scopus.com/inward/record.url?scp=85120951849&partnerID=8YFLogxK

U2 - 10.1007/s11005-021-01487-x

DO - 10.1007/s11005-021-01487-x

M3 - Article

AN - SCOPUS:85120951849

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 6

M1 - 148

ER -