On the Uniqueness of Ghost-Free Multi-Gravity -- II: Constraining antisymmetrised multi spin-2 interactions
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| Format: | Preprint |
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2026
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| _version_ | 1866914461031333888 |
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| author | Flinckman, Joakim Hassan, S. F. |
| author_facet | Flinckman, Joakim Hassan, S. F. |
| contents | So far, only a single theory of multiple spin-2 fields is known that features genuine multi-field interactions while remaining free of Boulware-Deser-type ghost instabilities. In this paper we show that this is the most general ghost-free multi spin-2 interaction type possible. We start with the general class of multivielbein interactions containing antisymmetrised products of vielbeins, considered earlier by Hinterbichler and Rosen. We formulate a necessary condition for these theories to be ghost-free. For two vielbeins the theory parameters remain unrestricted, reproducing the ghost-free bimetric theory. But for more than two vielbeins with genuine multi-field interactions, we show that the couplings are restricted precisely to yield the known ghost-free multivielbein theory, thus establishing its uniqueness. We also show that more general interactions, constructed using the ghost-free bimetric and multivielbein potentials as building blocks, satisfy the necessary ghost-free conditions provided the associated interaction graphs have a tree structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07625 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness of Ghost-Free Multi-Gravity -- II: Constraining antisymmetrised multi spin-2 interactions Flinckman, Joakim Hassan, S. F. High Energy Physics - Theory General Relativity and Quantum Cosmology So far, only a single theory of multiple spin-2 fields is known that features genuine multi-field interactions while remaining free of Boulware-Deser-type ghost instabilities. In this paper we show that this is the most general ghost-free multi spin-2 interaction type possible. We start with the general class of multivielbein interactions containing antisymmetrised products of vielbeins, considered earlier by Hinterbichler and Rosen. We formulate a necessary condition for these theories to be ghost-free. For two vielbeins the theory parameters remain unrestricted, reproducing the ghost-free bimetric theory. But for more than two vielbeins with genuine multi-field interactions, we show that the couplings are restricted precisely to yield the known ghost-free multivielbein theory, thus establishing its uniqueness. We also show that more general interactions, constructed using the ghost-free bimetric and multivielbein potentials as building blocks, satisfy the necessary ghost-free conditions provided the associated interaction graphs have a tree structure. |
| title | On the Uniqueness of Ghost-Free Multi-Gravity -- II: Constraining antisymmetrised multi spin-2 interactions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.07625 |