On the quantum field theory of the gravitational interactions

Sur la théorie quantique des champs des interactions gravitationnelles

Damiano Anselmi (1)

1 Dipartimento di Fisica dell'Università di Pisa and INFN

We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the $S$ matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical poles of the higher-derivative propagators and turning them into Lee-Wick poles. The Lagrangian of the simplest theory of quantum gravity based on this idea is the linear combination of $R$, $R_{\mu \nu}R^{\mu \nu }$, $R^{2}$ and the cosmological term. Only the graviton propagates in the cutting equations and, when the cosmological constant vanishes, the $S$ matrix is unitary. The theory satisfies the locality of counterterms and is renormalizable by power counting. It is unique in the sense that it is the only one with a dimensionless gauge coupling.

Mots clés: Quantum gravity; Quantum field theory; Renormalization; Unitarity; Cutting equations; Fakeons; Lee-Wick models

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Relativité Générale et Cosmologie Quantique [gr-qc]

Damiano Anselmi. On the quantum field theory of the gravitational interactions. Journal of High Energy Physics, 2017, 2017 (6), ⟨10.1007/JHEP06(2017)086⟩. ⟨hal-01900209⟩