Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D
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=3 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 ε = 4 − d and in 1/n 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) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.