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.
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- 1 Johan Henriksson,
- 2 Stefanos R. Kousvos,
- 3 Andreas Stergiou
- 1 University of Oxford
- 2 Πανεπιστήμιο Κρήτης / University of Crete [UOC]
- 3 Los Alamos National Laboratory [LANL]
- CERN (through Organization: Organisation européenne pour la recherche nucléaire / European Organization for Nuclear Research [CERN])
- Gouvernement du Canada / Government of Canada
- Hellenic Foundation for Research and Innovation [HFRI]
- Los Alamos National Laboratory [LANL]
- Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])
- Simons Foundation
- United States Department of Energy [DOE]