On mixed 't Hooft anomalies of emergent symmetries

In this paper, we investigate the dynamical constraints imposed on the UV theory when it develops an emergent symmetry in the infrared with mixed 't Hooft anomalies. We demonstrate that, under certain conditions, the UV theory must contain non-genuine operators. Our primary examples illustrating this phenomenon are 2D gauged linear sigma models and 3D Chern-Simons-matter theories. Through this analysis, we establish connections between different classes of topological quantum field theories and propose a correspondence between quantum cohomologies of distinct target spaces.