Abstract
In this final section, we consider the application of these ideas to theories exhibiting limit cycles. This requires an extension of the formalism of Weyl consistency conditions and the local renormalisation group to theories with global symmetries. It leads to important consequences for both the issue of whether scale invariant theories are necessarily conformal and for the nature of the space of couplings.
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Notes
- 1.
It is understood here that ω is always taken in the appropriate representation, without explicit notation. Similarly for other elements of G F , in particular A μ .
- 2.
This is reminiscent of the conditions for conformal invariance in 2-dim string-related non-linear sigma models. It was shown in [4, 33] that in these models, the condition for the absence of a conformal anomaly involves not the usual beta functions, but generalisations which are invariant under spacetime diffeomorphism invariance, which appears as a ‘flavour’ symmetry of the target space for the sigma model fields defined over the 2-dim worldsheet.
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Shore, G. (2017). Global Symmetries and Limit Cycles. In: The c and a-Theorems and the Local Renormalisation Group. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-54000-9_9
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DOI: https://doi.org/10.1007/978-3-319-54000-9_9
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