Abstract
This chapter motivates the study of scale invariant fixed points, and explains why scale invariance is generically enhanced to conformal invariance.
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Notes
- 1.
Recall that relevant (irrelevant) operators are those of dimension \(\Delta <D\) (\(\Delta >D\)). Operators of dimension \(\Delta =D\) are called marginal.
- 2.
Some of these constants are regulator-dependent. E.g. in dimensional regularization we have \(c_1=c_3=c_5=0\).
- 3.
Another problem with asymptotic safety in gravity, as opposed to QFT, is that the very meaning of the fixed point is unclear in this case. In quantum field theory, fixed points can be defined axiomatically through the CFT, as we will see later in these chapters, so the ERG is just one of the many ways to get at something which exists independently of the ERG. In case of gravity the fixed point is, until now, defined through the ERG manipulations, and an independent axiomatic definition is unknown. Finding such a definition is very important if one hopes to put asymptotic safety on solid ground.
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Rychkov, S. (2017). Physical Foundations of Conformal Symmetry. In: EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43626-5_1
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