General Properties of Multiscalar RG Flows in $d=4\varepsilon$
Abstract
Fixed points of scalar field theories with quartic interactions in $d=4\varepsilon$ dimensions are considered in full generality. For such theories it is known that there exists a scalar function $A$ of the couplings through which the leadingorder betafunction can be expressed as a gradient. It is here proved that the fixedpoint value of $A$ is bounded from below by a simple expression linear in the dimension of the vector order parameter, $N$. Saturation of the bound requires a marginal deformation, and is shown to arise when fixed points with the same global symmetry coincide in coupling space. Several general results about scalar CFTs are discussed, and a review of known fixed points is given.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.10541
 Bibcode:
 2018arXiv181010541R
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics
 EPrint:
 29 pages, 4 figures