Self-dual gravity from higher-spin theory

V. E. Didenko; A. V. Korybut

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arXiv · 2603.21822

Self-dual gravity from higher-spin theory

V. E. Didenko·A. V. Korybut

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Abstract

Higher-spin symmetry is known to mix lower-spin fields with higher-spin fields, creating a complex interaction picture where no closed finite field sector is expected to exist for dimensions greater than three. By studying the self-dual part of higher-spin interaction vertices in four dimensions, we show that gauge fields of spins greater than two can be consistently set to zero. In this case, the fields with helicities $-2\leqλ\leq 0$ form a closed sub-sector and also act as sources for positive helicities. For these lower spin fields, we identify their equations of motion. In particular, we show that self-dual gravity with a cosmological constant emerges as a unique rigid part of higher-spin interactions. Notably, its equations have a form that incorporates the Moyal star product, which is essential for generating the higher-spin algebra. Therefore, we demonstrate that self-dual gravity can be derived from higher-spin symmetries.

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V. E. Didenko, A. V. Korybut. 2026-05-12. Self-dual gravity from higher-spin theory. https://arxiv.org/abs/2603.21822

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