Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Abstract

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n)O(m)×O(n) global symmetry in d=3d=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-dε=4−d and in 1/n1/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)O(2)×O(n) theories for various values of nn. Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilonε and large-nn expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.