Chiral higher spin gravity

We construct a candidate for the most general chiral higher spin theory with AdS(3) 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'' AdS(3) boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a W-3 algebra on the left and an affine sl(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