Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

We consider the two-dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for s >= 34, the water waves system is locally well-posed in Hs, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru. It is also a 14 improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru.