  We use the conformal bootstrap program to derive necessary conditions for
emergent symmetry enhancement from discrete symmetry (e.g. $\mathbb{Z}_n$) to
continuous symmetry (e.g. $U(1)$) under the renormalization group flow. In
three dimensions, in order for $\mathbb{Z}_2$ symmetry to be enhanced to $U(1)$
symmetry, the conformal bootstrap program predicts that the scaling dimension
of the order parameter field at the infrared conformal fixed point must satisfy
$\Delta_1 > 1.08$. We also obtain the similar conditions for $\mathbb{Z}_3$
symmetry with $\Delta_{1} > 0.580$ and $\mathbb{Z}_4$ symmetry with $\Delta_1 >
0.504$ from the simultaneous conformal bootstrap analysis of multiple
four-point functions. Our necessary conditions impose severe constraints on
many controversial physics such as the chiral phase transition in QCD, the
deconfinement criticality in N\'eel-VBS transitions and anisotropic
deformations in critical $O(n)$ models. In some cases, we find that the
conformal bootstrap program dashes hopes of emergent symmetry enhancement
proposed in the literature.
