Chong Wang

We propose a new type of critical quantum liquids, dubbed Stiefel liquids, based on 2+1 dimensional Wess-Zumino-Witten models on target space SO(N)/SO(4). We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N = 5 and N = 6, respectively. Furthermore, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that the theories do not (at least not easily) admit any weakly-coupled UV completion.