Bootstrap bounds on conformal field theories with Lieb-Schultz-Mattis anomalies

We put bounds on 1+1d conformal field theories (CFTs) that saturate certain mixed anomalies arising in spin chains subject to the Lieb-Schultz-Mattis (LSM) theorem using conformal bootstrap techniques. To do this, we will present a new hybrid bootstrap approach, which augments modular bootstrap by additionally imposing crossing symmetry on correlation functions of certain symmetry defect operators. The hybrid bootstrap accounts for a more complete picture of 't Hooft anomalies of discrete symmetries in 1+1d CFTs than modular bootstrap alone and still gives universal bounds on local operators. In particular, we will present universal bounds on charged operators, some of which are only possible with our hybrid approach. Our bounds exhibit distinctive kinks, some of which are approximately saturated by known theories such as the su(3) level 1 WZW model, and others which are unexplained.