Constraints on beta functions in field theories
Abstract
The $\beta$functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings allowed by symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow takes place in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $\beta$functions defined in a measure zero subspace of couplings completely determine the $\beta$functions in the entire space of couplings. We provide a quantum renormalization groupbased algorithm for reconstructing the full $\beta$functions from the $\beta$functions defined in the subspace. The general prescription is applied to two simple examples.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.11880
 Bibcode:
 2020arXiv200911880M
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 61 pages, 12 figures, review of Wilsonian RG added