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arXiv · 1803.00859

Renormalization group properties of the conformal mode of a torus

Matthew P. Kellett·Tim R. Morris
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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.

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Matthew P. Kellett, Tim R. Morris. 2018-03-02. Renormalization group properties of the conformal mode of a torus. https://doi.org/10.1088/1361-6382%2Faad06e

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