Abstract
Unitarity of the scale-invariant coupled theory of higher-derivative gravity and matter is investigated. A scalar field coupled with a Dirac fermion is taken as the matter sector. Following the idea of induced gravity the 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. The scalar field develops a new minimum via the Coleman–Weinberg procedure inducing the Newton constant and masses in the matter sector. The spin-2 problematic ghost and the spin-0 mode of the metric fluctuation get a mass in the broken phase of the theory. The energy dependence of the vacuum expectation value 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 the initial parameters. The induced Newton constant is seen to vanish in the ultraviolet case. By properly choosing parameters it is possible to make the matter fields physically unrealisable.
Highlights
In this paper, motivated by the results of [2,3,4,5,6,7,8] we study the scale-invariant higher-derivative gravitational system coupled with matter fields
The one-loop RG improved effective potential for the scalar field is computed by incorporating the quantum fluctuations of both matter and gravity [55]
As the ghost action does not depend on the background scalar field φ, there is no contribution by the ghost to the effective potential, and will be ignored in the following
Summary
In this paper, motivated by the results of [2,3,4,5,6,7,8] we study the scale-invariant higher-derivative gravitational system coupled with matter fields. The one-loop RG improved effective potential for the scalar field is computed by incorporating the quantum fluctuations of both matter and gravity [55]. The scale invariance is broken dynamically when the scalar field φ acquires a VeV via Coleman–Weinberg mechanism [46] This in turn induces the gravitational Newton constant, the cosmological constant and masses in the matter sector. one-loop renormalisation group improved effective potential for the scalar field is computed by incorporating quantum corrections from the gravitational and matter degrees of freedom. the breaking of scale invariance is studied via Coleman–Weinberg mechanism, which in turn induces the gravitational Newton constant and masses in the broken phase.
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