Seeking fixed points in multiple coupling scalar theories in the \(\epsilon\) expansion

DOI10.1007/JHEP05(2018)051zbMATH Open1391.81172arXiv1707.06165OpenAlexW3105212459MaRDI QIDQ1651096

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Publication date: 11 July 2018

Published in: (Search for Journal in Brave)

Abstract: Fixed points for scalar theories in $4-varepsilon$, $6-varepsilon$ and $3-varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, $O(N)$, is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the $a$-theorem are used to help classify potential fixed points. At lowest order in the $varepsilon$-expansion it is shown that at fixed points there is a lower bound for $a$ which is saturated at bifurcation points.

Full work available at URL: https://arxiv.org/abs/1707.06165

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