Exorcising Ghosts in Induced Gravity

TL;DR

This paper investigates the unitarity of scale-invariant higher-derivative gravity coupled with matter, demonstrating how dynamical symmetry breaking induces Einstein-Hilbert terms, masses for problematic modes, and explores conditions to evade ghost issues.

Contribution

It introduces a mechanism where dynamical symmetry breaking in scale-invariant higher-derivative gravity generates Einstein-Hilbert action and addresses ghost problems through parameter choices.

Findings

The scalar field develops a new minimum via Coleman-Weinberg mechanism.

The spin-2 ghost can be evaded by keeping its mass above the energy scale.

Induced Newton's constant vanishes in the ultraviolet regime.

Abstract

Unitarity of scale-invariant coupled theory of higher-derivative gravity and matter is investigated. A scalar field coupled with dirac fermion is taken as matter sector.Following the idea of induced gravity Einstein-Hilbert term is generated via dynamical symmetry breaking of scale-invariance. The renormalisation group flows are computed and one-loop RG improved effective potential of scalar is calculated. Scalar field develops a new minimum via Coleman-Weinberg procedure inducing Newton's constant and masses in the matter sector. The spin-2 problematic ghost and the spin-0 mode of the metric fluctuation gets a mass in the broken phase of theory. The energy-dependence of VeV in the RG improved scenario implies a running for the induced parameters. This sets up platform to ask whether it is possible to evade the spin-2 ghost by keeping its mass always above the running energy scale? In broken phase this question is satisfactorily answered for a large domain of coupling parameter space where the ghost is evaded. The spin-0 mode can be made physically realisable or not depending upon the choice of initial parameters. Induced Newton's constant is seen to vanishes in ultraviolet. By properly choosing parameters it is possible to make the matter fields physically unrealisable.