Abstract
We consider four-dimensional quadratic gravity coupled to infinite towers of free massive scalar fields, Weyl fermions and vector bosons. We find that for specific numbers of towers, finite cosmological and Newton constants are induced in the 1-loop effective action. This is derived both in Adler's approach and by using the heat kernel method, which yield identical results. If the infinite number of massive states may be regarded as Kaluza–Klein modes arising from fields in higher dimensions, there are no Kaluza–Klein states associated with the four-dimensional graviton. Hence gravity is intrinsically four-dimensional.
Highlights
Induced gravity is an old proposal [1,2,3,4,5,6,7,8,9,10,11,12] according to which gravity is not fundamental but is rather induced by quantum effects from the matter content of the universe
In the induced gravity framework, one assumes a prescribed but not dynamical background on which matter fields are living. The latter are scalars, spinors and vectors coupled to the spacetime metric, which is clearly not dynamical as it appears with no derivatives
We have considered a four-dimensional gravity action based on four-derivative kinetic terms coupled to infinite towers of free massive scalar, fermionic and vector fields
Summary
Induced gravity is an old proposal [1,2,3,4,5,6,7,8,9,10,11,12] according to which gravity is not fundamental but is rather induced by quantum effects from the matter content of the universe. In order to justify that the induced gravity action is to be extremized with respect to the metric, it may be unavoidable to treat the graviton as a quantum field Another concern is that higher derivative terms of the metric are induced by the loops of matter fields. For infinite towers of matters states, we find that the Einstein action parameters Λind and Gind remain predictable This is achieved at the semiclassical level for the gravitational degrees of freedom and still holds at the 1-loop level. 2, treating the metric as a classical background, we derive in the context of Adler’s formalism the finite cosmological and Newton constants that are induced by integrating out infinite towers of free real scalars, Weyl fermions and vector bosons. More work for establishing whether this can be achieved is required
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