Lorentz violating quadratic gravity

TL;DR

This paper investigates how Lorentz symmetry violation, induced by a vector field in quadratic gravity, affects quantum renormalization and classical solutions, revealing that standard geometries like Schwarzschild and de Sitter remain solutions under certain conditions.

Contribution

It provides the first detailed one-loop renormalization analysis of Lorentz-violating quadratic gravity and identifies classical solutions compatible with Lorentz violation.

Findings

Derived counterterms for renormalization in Lorentz-violating quadratic gravity.

Showed Schwarzschild and de Sitter solutions persist with specific bumblebee configurations.

Analyzed the impact of Lorentz violation on the UV structure of gravity theories.

Abstract

In this paper, we explore the perturbative renormalization and study the classical dynamics of the bumblebee model coupled to quadratic gravity, a theoretical setting that allows the violation of Lorentz symmetry. Such a violation arises from a vector field whose potential is engineered to induce a nonzero vacuum expectation value (VEV), thereby leading to the emergence of a preferred direction in spacetime and, consequently, to the spontaneous breaking of Lorentz symmetry. Working in dimensional regularization and expanding the metric around flat space, we compute the one-loop divergent parts of the two-point functions of the bumblebee and graviton fields, with special emphasis on the role of Lorentz-violating insertions in internal lines. These results determine the counterterms required to renormalize the gravitational and bumblebee sectors in the presence of a preferred background direction, and make explicit how Lorentz-violating interactions feed back into the UV structure of quadratic gravity. On the classical side, we derive the field equations and identify exact solutions supported by bumblebee backgrounds. In particular, we show that the Schwarzschild and de Sitter geometries remain exact solutions for an appropriate bumblebee field profile, even in the presence of one of the non-minimal couplings. We close with a discussion of the operator content suggested by the one-loop structure and of prospective extensions to cosmological and less symmetric backgrounds.