SciPost Phys. 6, 008 (2019) ·
published 17 January 2019

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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.
SciPost Phys. 5, 050 (2018) ·
published 22 November 2018

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We study complex CFTs describing fixed points of the twodimensional
$Q$state Potts model with $Q>4$. Their existence is closely related to the
weak firstorder phase transition and walking RG behavior present in the real
Potts model at $Q>4$. The Potts model, apart from its own significance, serves
as an ideal playground for testing this very general relation. Cluster
formulation provides nonperturbative definition for a continuous range of
parameter $Q$, while Coulomb gas description and connection to minimal models
provide some conformal data of the complex CFTs. We use one and twoloop
conformal perturbation theory around complex CFTs to compute various properties
of the real walking RG flow. These properties, such as drifting scaling
dimensions, appear to be common features of the QFTs with walking RG flows, and
can serve as a smoking gun for detecting walking in Monte Carlo simulations.
The complex CFTs discussed in this work are perfectly well defined, and can
in principle be seen in Monte Carlo simulations with complexified coupling
constants. In particular, we predict a pair of $S_5$symmetric complex CFTs
with central charges $c\approx 1.138 \pm 0.021 i$ describing the fixed points
of a 5state dilute Potts model with complexified temperature and vacancy
fugacity.
SciPost Phys. 2, 001 (2017) ·
published 10 February 2017

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We discuss the 4pt function of the critical 3d Ising model, extracted from
recent conformal bootstrap results. We focus on the nongaussianity Q  the
ratio of the 4pt function to its gaussian part given by three Wick
contractions. This ratio reveals significant nongaussianity of the critical
fluctuations. The bootstrap results are consistent with a rigorous inequality
due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.