TY - JOUR
T1 - Braided symmetries in noncommutative field theory
AU - Giotopoulos, Grigorios
AU - Szabo, Richard J.
N1 - Funding Information:
We thank Marija Dimitrijević Ćirić, Larisa Jonke, Voja Radovanović, Alexander Schenkel and Francesco Toppan for helpful discussions and correspondence. RJS thanks the editors Paolo Aschieri, Edwin Beggs, Francesco D’Andrea, Emil Prodan and Andrzej Sitarz for the invitation to contribute to this special issue. The work of G.G. was supported by a Doctoral Training Grant from the UK Engineering and Physical Sciences Research Council. The work of RJS was supported by the Consolidated Grant ST/P000363/1 from the UK Science and Technology Facilities Council.
Publisher Copyright:
© 2022 IOP Publishing Ltd.
PY - 2022/9/2
Y1 - 2022/9/2
N2 - 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.
AB - 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.
KW - Drinfel'd twists
KW - Homotopy algebras
KW - Noncommutative field theory
UR - http://www.scopus.com/inward/record.url?scp=85136014026&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ac5dad
DO - 10.1088/1751-8121/ac5dad
M3 - Review article
AN - SCOPUS:85136014026
SN - 1751-8113
VL - 55
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 35
M1 - 353001
ER -