On-shell gauge invariant three-point amplitudes

A bstract Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields wit...

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Veröffentlicht in:The journal of high energy physics 2017-12, Vol.2017 (12), p.1-26, Article 48
Hauptverfasser: Sun, Zhengdi, Xu, Hui, Cheung, Yeuk-Kwan E.
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Sprache:eng
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Zusammenfassung:A bstract Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches. Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field ϕ and an antisymmetric rank-2 tensor field A μν . Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2017)048