Abstract
We construct actions for four dimensional noncommutative Yang-Mills theory with star-gauge symmetry, with non-constant noncommutativity, to all orders in the noncommutativity. Our construction covers all noncommutative spaces corresponding to Drinfel’d twists based on the Poincaré algebra, including nonabelian ones, whose r matrices are unimodular. This includes particular Lie-algebraic and quadratic noncommutative structures. We prove a planar equivalence theorem for all such noncommutative field theories, and discuss how our actions realize twisted Poincaré symmetry, as well as twisted conformal and twisted supersymmetry, when applicable. Finally, we consider noncommutative versions of maximally supersymmetric Yang-Mills theory, conjectured to be AdS/CFT dual to certain integrable deformations of the AdS5 × S5 superstring.
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Acknowledgments
We would like to thank Riccardo Borsato, Ben Hoare, Anna Pachoł, and Richard Szabo for discussions, and Richard Szabo for valuable comments on the draft. TM’s research is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory”. The work of ST is supported by the German Research Foundation via the Emmy Noether program “Exact Results in Extended Holography”. ST is supported by LT.
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Meier, T., van Tongeren, S.J. Gauge theory on twist-noncommutative spaces. J. High Energ. Phys. 2023, 45 (2023). https://doi.org/10.1007/JHEP12(2023)045
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DOI: https://doi.org/10.1007/JHEP12(2023)045