Gauging the higher-spin-like symmetries by the Moyal product. (English) Zbl 1466.81057
Summary: We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by L. Bonora et al. [J. High Energy Phys. 2016, No. 12, Paper No. 84, 70 p. (2016; Zbl 1390.83264) and J. High Energy Phys. 2018, No. 1, Paper No. 80, 40 p. (2018; Zbl 1384.83037)] in their studies of linear coupling of matter fields to an infinite tower of higher spin fields. The off-shell definition is based on fields defined on a \(2d\)-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. Using this algebra we construct well-defined weakly non-local actions, both in the gauge and the matter sector, by mimicking the Yang-Mills procedure. The theory allows for a description in terms of an infinite tower of higher spin spacetime fields only on-shell. Interestingly, Euclidean theory allows for such a description also off-shell. Owing to its formal similarity to non-commutative field theories, the formalism allows for the introduction of a covariant potential which plays the role of the generalised vielbein. This covariant formulation uncovers the existence of other phases and shows that the theory can be written in a matrix model form. The symmetries of the theory are analyzed and conserved currents are explicitly constructed. By studying the spin-2 sector we show that the emergent geometry is closely related to teleparallel geometry, in the sense that the induced linear connection is opposite to Weitzenböck’s.
MSC:
| 81T11 | Higher spin theories |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C45 | Quantization of the gravitational field |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 83C65 | Methods of noncommutative geometry in general relativity |
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