Marten Reehorst, Slava Rychkov, David SimmonsDuffin, Benoit Sirois, Ning Su, Balt van Rees
SciPost Phys. 11, 072 (2021) ·
published 28 September 2021

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Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information “allowed”/“excluded” with a continuous “navigator” function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore highdimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are welldefined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasiNewton optimization methods, which we illustrate by navigating towards the 3d Ising island.
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.
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