Bootstrapping the O(3) Model from Dimensions 2 to 3

We present the results of a numerical conformal bootstrap study of the O(3) model in dimensions between 2 and 3. In 3 dimensions, the O(3) model comes in two flavors according to whether or not hedgehog topological defects are allowed or suppressed. The hedgehog-suppressed model is of interest as the prototypical deconfined quantum critical point. While the O(N) fixed point in 3 dimensions is strongly coupled and thus not immediately amenable to study, one can gain perturbative control of the problem by working in 2+epsilon dimensions. One can thus ask whether this 2+epsilon expansion breaks down at some intermediate dimension or whether it can be followed up to d=3. If the latter, does it access the hedgehog-allowed O(3) model or something else? We use the numerical conformal bootstrap to study these questions by following the evolution of O(3) model from near dimension 2 to dimension 3.