SciPost Phys. 6, 035 (2019) ·
published 21 March 2019
Three-dimensional theories with cubic symmetry are studied using the
machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity
are imposed on a set of mixed correlators, and various aspects of the parameter
space are probed for consistency. An isolated allowed region in parameter space
is found under certain assumptions involving pushing operator dimensions above
marginality, indicating the existence of a conformal field theory in this
region. The obtained results have possible applications for ferromagnetic phase
transitions as well as structural phase transitions in crystals. They are in
tension with previous $\varepsilon$ expansion results, as noticed already in
SciPost Phys. 6, 008 (2019) ·
published 17 January 2019
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 leading-order beta-function can be expressed as a gradient.
It is here proved that the fixed-point 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.
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