SciPost Phys. 15, 075 (2023) ·
published 31 August 2023
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Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs are analyzed in $d=4-\varepsilon$ and $d=3$. This includes perturbative computations in the $\varepsilon$ and large-$n$ expansions as well as non-perturbative ones with the numerical conformal bootstrap. New perturbative results are presented and a variety of non-perturbative bootstrap bounds are obtained in $d=3$. Various features of the bounds obtained for large values of $n$ disappear for low values of $n$ (keeping $m<n$ fixed), a phenomenon which is attributed to a transition of the corresponding fixed points to the non-unitary regime. Numerous bootstrap bounds are found that are saturated by large-$n$ results, even in the absence of any features in the bounds. A double scaling limit is also observed, for $m$ and $n$ large with $m/n$ fixed, both in perturbation theory as well as in the numerical bootstrap. For the case of two-flavor massless QCD existing bootstrap evidence is reproduced that the chiral phase transition may be second order, albeit associated to a universality class unrelated to the one usually discussed in the $\varepsilon$ expansion. Similar evidence is found for the case of three-flavor massless QCD, where we observe a pronounced kink.
SciPost Phys. 12, 206 (2022) ·
published 28 June 2022
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The recent emergence of the modern conformal bootstrap method for the study
of conformal field theories (CFTs) has enabled the revisiting of old problems
in classical critical phenomena described by three-dimensional CFTs. The study
of such CFTs with $O(m)^n \rtimes S_n$ global symmetry, also known as MN
models, is pursued in this work. Systems of mixed correlators involving scalar
operators in two different representations of the global symmetry group are
considered. Isolated allowed regions are found in parameter space for various
values of $m$ and $n$. These "islands" can be separated into two qualitative
groups: those close to the unitarity bound and those further away. As a
by-product of our analysis generic tensor structures required to bootstrap any
$G^n \rtimes S_n$ theory with $G$ arbitrary are worked out.
Dr Kousvos: "We thank the referee for a car..."
in Submissions | report on CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD