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No-go theorems for unitary and interacting partially massless spin-two fields.
Euihun Joung1, Wenliang Li1, Massimo Taronna2
1AstroParticule et Cosmologie, Unité Mixte de Recherche 7164 du CNRS, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
Physical Review Letters
|September 13, 2014
Summary
A partially massless spin-two field interacting with gravity cannot form a unitary theory. Theories with positive kinetic terms lead to imaginary coupling constants, while negative terms recover conformal gravity.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Investigating theories of partially massless (PM) spin-two fields interacting with gravity is crucial for understanding fundamental forces.
- The behavior of such fields in four-dimensional spacetime requires detailed theoretical analysis.
Purpose of the Study:
- To examine the generic theory of a partially massless spin-two field interacting with gravity.
- To determine the conditions for the existence of a unitary theory and analyze its properties.
Main Methods:
- Analysis of the most general form of the Lagrangian for a PM spin-two field coupled to gravity.
- Investigation of de Sitter backgrounds and their associated global symmetries (so(1,5) or so(2,4)).
- Examination of the PM cubic self-interaction and its coupling constant.
Main Results:
- A de Sitter background requires so(1,5) or so(2,4) symmetry based on the sign of kinetic terms.
- A positive sign necessitates a purely imaginary coupling constant for PM cubic self-interaction.
- A negative sign leads to the recovery of conformal gravity.
Conclusions:
- A unitary theory of a PM spin-two field coupled to Einstein gravity with a perturbatively local Lagrangian cannot exist.
- The PM limit of massive gravity also lacks PM gauge symmetry.
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