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Abstract: Just like the vector bosons in Abelian and non-Abelian gauge theories,gravitons can attain mass by spontaneous local symmetry breaking. The questionis whether this can happen in a Lorentz-invariant way. We consider the use offour scalar fields that break coordinate reparametrization invariance, byplaying the role of preferred flat coordinates x, y, z, and t. In the unbrokenrepresentation, the theory has a negative cosmological constant, which istuned to zero by the scalars in the broken phase. Massive spin 2 bosons and asingle massive scalar survive. The theory is not renormalizable, so at best itcan be viewed as an effective field theory for massive spin 2 particles. Onemay think of applications in cosmology, but a more tantalizing idea is to applyit to string theory approaches to QCD: if the gluon sector is to be describedby a compactified 26 or 10 dimensional bosonic string theory, then the ideasconsidered here could be used to describe the mechanism that removes a masslessor tachyonic scalar and provides mass to the spin 2 glueball states. Thedelicate problem of removing indefinite metric and-or negative energy states isaddressed. The scalar particle has negative metric, so that unitarity demandsthat only states with an even number of them are allowed. Various ways areconsidered to adapt the matter section of the theory such that matter onlycouples to positive metric states, and we succeed in suppressing the maincontributions to unitarity-violating amplitudes, but the exact restoration ofunitarity in the spinless sector will continue to be a delicate issue intheories of this sort.

Autor: Gerard 't Hooft

Fuente: https://arxiv.org/

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