Renormalization group properties of the conformal mode of a torus

Abstract

The Wilsonian renormalization group properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. If couplings are chosen so that the quantum field theory exists on ${\mathbb{R}}^4$, it fails to exist on manifolds below a certain size, if a certain universal shape function turns negative. We demonstrate that this is triggered by inhomogeneity in the cases of ${\mathbb{T}}^4$ and ${\mathbb{T}}^3\times \mathbb{R}$, including twisted versions. Varying the moduli, we uncover a rich phenomenology.

arXiv comment25 pages, 5 figures; version to be published in Class. Quantum Grav

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Cited by in corpus (8)

• BRST in the Exact RG
• Renormalization group properties of the conformal sector: towards perturbatively renormalizable quantum gravity
• Quantum gravity, renormalizability and diffeomorphism invariance
• Provable properties of asymptotic safety in $f(R)$ approximation
• Structure of Correlated Worldline Theories of Quantum Gravity
• The continuum limit of quantum gravity at first order in perturbation theory
• The continuum limit of quantum gravity at second order in perturbation theory
• The continuum limit of the conformal sector at second order in perturbation theory