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Effective Potential for Conformal Factor and GL(4) Symmetry

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arxiv 2401.04712 v1 pith:G3CYM7AE submitted 2024-01-09 hep-th gr-qc

Ichiro Oda This is my paper · ORCID
classification hep-thgr-qc
keywords conformaleffectivefactorpotentialexpectationnon-vanishingsymmetryvacuum
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abstract

We revisit the issue that the effective potential for the conformal factor of the metric, which is generated by quantized matter fields, possesses a non-vanishing vacuum expectation value (VEV) or not. We prove that the effective potential has a vanishing vacuum expectation value on the basis of a global $GL(4)$ symmetry. We also account for the reason why there seem to be two different effective potentials for the conformal factor in a theory, one of which gives rise to a vanishing VEV for the conformal factor whereas the other does a non-vanishing VEV.

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Cited by 1 Pith paper

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  1. Spacetime and Planck mass generation from scale-invariant degenerate gravity

    hep-th 2024-11 reject novelty 5.0 of 10

    The paper computes a one-loop effective potential that can produce a Planck mass from a scalar vacuum, but the curvature that seeds it is assumed by hand and the vierbein scale factor runs away.

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