Abstract
We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the ϕ i × ϕ j OPE, where ϕ i is a fundamental of O(N ). Comparing these bounds to previous determinations of critical exponents in the O(N ) vector models, we find strong numerical evidence that the O(N ) vector models saturate the bootstrap constraints at all values of N . We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N ) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N .
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Kos, F., Poland, D. & Simmons-Duffin, D. Bootstrapping the O(N ) vector models. J. High Energ. Phys. 2014, 91 (2014). https://doi.org/10.1007/JHEP06(2014)091
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DOI: https://doi.org/10.1007/JHEP06(2014)091