3 years ago

# Quantum implications of a scale invariant regularisation.

D. M. Ghilencea

We study scale invariance at the quantum level in a perturbative approach. For a scale-invariant classical theory the scalar potential is computed at three-loop level while keeping manifest this symmetry. Spontaneous scale symmetry breaking is transmitted at quantum level to the visible sector (of $\phi$) by the associated Goldstone mode (dilaton $\sigma$) which enables a scale-invariant regularisation and whose vev $\langle\sigma\rangle$ generates the subtraction scale ($\mu$). While the hidden ($\sigma$) and visible sector ($\phi$) are classically decoupled in $d=4$ due to an enhanced Poincar\'e symmetry, they interact through (a series of) evanescent couplings $\propto\epsilon$, dictated by the scale invariance of the action in $d=4-2\epsilon$. At the quantum level these couplings generate new corrections to the potential, as scale-invariant non-polynomial effective operators $\phi^{2n+4}/\sigma^{2n}$. These are comparable in size to "standard" loop corrections and important for values of $\phi$ close to $\langle\sigma\rangle$. For $n=1,2$ the beta functions of their coefficient are computed at three-loops. In the IR limit dilaton fluctuations decouple, the effective operators are suppressed by large $\langle\sigma\rangle$ and the effective potential becomes that of a renormalizable theory with explicit scale symmetry breaking by the DR scheme (of $\mu=$constant).

Publisher URL: http://arxiv.org/abs/1712.06024

DOI: arXiv:1712.06024v2

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