Conformal Bootstrap Dashing Hopes of Emergent Symmetry

Understand

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 $\Delta_1 > 1.08$.