Symmetries from Locality. II. Gravitation and Lorentz Boosts

Abstract

It is known that local, Lorentz invariant, unitary theories involving particles with spin 1 demand that the matter sector they couple to are organized by internal physical symmetries and the associated charge conservation, while spin 3/2 demands supersymmetry. However, the introduction of a spin 2 graviton does not obviously demand new symmetries of the matter sector (although it does demand a universal coupling). In this work we relax the assumption of Lorentz boost symmetry, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. This extends and complements our accompanying work in Part 1 on related issues for spin 1 particles in electromagnetism. In order to avoid potential problems with longitudinal modes of the graviton, we choose to project them out, leaving only two degrees of freedom. We study large classes of theories that a priori may violate Lorentz boost invariance. By requiring the tree-level exchange action be local, we find that consistency demands that the Lorentz boost symmetry must be satisfied by the graviton and the matter sector, and in turn we recover general relativity at this order of analysis.

arXiv comment13 pages in double column format. V2 further clarification and fixed some typos. V3: Further clarifications, including mass terms. Updated towards version accepted for publication in Phys. Rev. D, including journal title format

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• Bound on Quantum Fluctuations in Gravitational Waves from LIGO-Virgo
• Acausality in Superfluid Dark Matter and MOND-like Theories
• Causal Modifications of Gravity and Their Observational Bounds
• Symmetries from Locality. I. Electromagnetism and Charge Conservation
• Symmetries from Locality. III. Massless Spin 2 Gravitons and Time Translations