SciPost Phys. 11, 015 (2021) ·
published 16 July 2021
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Fixed points in three dimensions described by conformal field theories with
$MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in
critical phenomena. Associated experimental data for $m=n=2$ suggest the
existence of two non-trivial fixed points, while the $\varepsilon$ expansion
predicts only one, resulting in a puzzling state of affairs. A recent numerical
conformal bootstrap study has found two kinks for small values of the
parameters $m$ and $n$, with critical exponents in good agreement with
experimental determinations in the $m=n=2$ case. In this paper we investigate
the fate of the corresponding fixed points as we vary the parameters $m$ and
$n$. We find that one family of kinks approaches a perturbative limit as $m$
increases, and using large spin perturbation theory we construct a large $m$
expansion that fits well with the numerical data. This new expansion, akin to
the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed
point found in the $\varepsilon$ expansion. For the other family of kinks, we
find that it persists only for $n=2$, where for large $m$ it approaches a
non-perturbative limit with $\Delta_\phi\approx 0.75$. We investigate the
spectrum in the case $MN_{100,2}$ and find consistency with expectations from
the lightcone bootstrap.
Johan Henriksson, Stefanos R. Kousvos, Andreas Stergiou
SciPost Phys. 9, 035 (2020) ·
published 10 September 2020
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Motivated by applications to critical phenomena and open theoretical
questions, we study conformal field theories with $O(m)\times O(n)$ global
symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical
bootstrap techniques. Using the analytic bootstrap, we calculate anomalous
dimensions and OPE coefficients as power series in $\varepsilon=4-d$ and in
$1/n$, with a method that generalizes to arbitrary global symmetry. Whenever
comparison is possible, our results agree with earlier results obtained with
diagrammatic methods in the literature. Using the numerical bootstrap, we
obtain a wide variety of operator dimension bounds, and we find several islands
(isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories
for various values of $n$. Some of these islands can be attributed to fixed
points predicted by perturbative methods like the $\varepsilon$ and large-$n$
expansions, while others appear to arise due to fixed points that have been
claimed to exist in resummations of perturbative beta functions.
Dr Henriksson: "We thank the reviewer for thei..."
in Submissions | report on Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry