Before revision:  In a recent paper Krauthgamer, Lee and Rika SODA19 showed an upper bound of O(\log \gamma) on the distortion, improving previous results by Lee and Sidiropoulos [STOC09] and Chekuri et . al. [J.Comb.
After revision:  In a recent paper Krauthgamer, Lee and Rika  showed an upper bound of O(\log \gamma) on the distortion, improving previous results by Lee and Sidiropoulos [STOC09] and Chekuri et . al. [J.Comb.