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arXiv · 2210.07130

Higher-spin Yang-Mills, amplitudes and self-duality

Tim Adamo·Tung Tran
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Abstract

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang-Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory, and use it to derive the formula for the MHV amplitude.

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Tim Adamo, Tung Tran. 2022-10-13. Higher-spin Yang-Mills, amplitudes and self-duality. https://doi.org/10.1007/s11005-023-01673-z

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