Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\varepsilon$ Expansion
Abstract
Fixed points for scalar theories in , and 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, , is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the -theorem are used to help classify potential fixed points. At lowest order in the -expansion it is shown that at fixed points there is a lower bound for which is saturated at bifurcation points.
Cite
@article{arxiv.1707.06165,
title = {Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\varepsilon$ Expansion},
author = {Hugh Osborn and Andreas Stergiou},
journal= {arXiv preprint arXiv:1707.06165},
year = {2019}
}
Comments
v1: 55 pages. v2: 58 pages; new fixed points in 4-{\epsilon} dimensions, further discussion of large-N behaviour in 3-{\epsilon} dimensions, additional references; v3: Typos fixed; v4: Added references. Version to appear in JHEP; v5: Minor emendations, references added. v6: 60 pages; typos fixed, some new results and references added. v7: 61 pages; some additions in section 5 and appendix B