Massive bigravity as a presymplectic BV-AKSZ sigma-model

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Summary

The paper proposes a presymplectic BV-AKSZ sigma-model formulation of massive bigravity, which encodes the ghost-free massive bigravity theory action and its Batalin-Vilkovisky extension in terms of finite-dimensional graded geometry of the target space.

Highlights

• The target space is a quasi-regular submanifold of a linear graded manifold, which is a direct product of two copies of the shifted Poincare or (anti-)de Sitter Lie algebra.
• The presymplectic structure and the compatible pre-Q structure are sums of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term.
• The constraints determining the submanifold are the super-geometrical realization of the known Deser-van Nieuwenhuizen condition and its descendant.
• The presymplectic BV-AKSZ formulation describes bigravity in three and four space-time dimensions.
• The construction gives a new insight into the geometrical structures underlying bigravity and potentially more general theories.
• The deformed and factorized structure of the graded manifold suggests that other interesting theories could exhibit the same hidden structure.
• The presymplectic BV-AKSZ formulation can be used to study consistent interactions between gauge fields.

Key Insights

• The presymplectic BV-AKSZ formulation provides a concise and geometrical description of massive bigravity, which is a complex theory that combines two interacting spin-2 fields.
• The use of a quasi-regular submanifold as the target space allows for a more symmetric and elegant formulation of the theory, which is not possible in the standard BV formulation.
• The constraints imposed on the submanifold are crucial in ensuring the correct spectrum and gauge invariance of the theory, and their super-geometrical realization provides a new insight into the underlying structure of bigravity.
• The presymplectic BV-AKSZ formulation can be used to study the consistent interactions between gauge fields, which is an important problem in theoretical physics.
• The deformed and factorized structure of the graded manifold underlying this formulation suggests that other interesting theories could exhibit the same hidden structure, which could lead to new insights and discoveries.
• The presymplectic BV-AKSZ formulation provides a new tool for studying massive deformations of supergravities, which is an important area of research in theoretical physics.
• The use of a presymplectic structure instead of a symplectic one allows for a more general and flexible formulation of the theory, which can be used to study a wide range of physical systems.

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Citation

Grigoriev, M., & Gritzaenko, V. (2024). Massive bigravity as a presymplectic BV-AKSZ sigma-model (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2410.13075