Chiral higher spin gravity

We construct a candidate for the most general chiral higher spin theory with AdS₃ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are 19 functions. Despite this, we show that the resulting metric has the form of the "most general" AdS₃ boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a W₃ algebra on the left and an affine s l (3 )_k current algebra on the right, as desired. The metric and higher spin fields depend on all the 19 functions. We compare our work with previous results in the literature.