Calabi-Yau black holes and (0,4) sigma models

When an M-theory fivebrane wraps a holomorphic surface P in a Calabi-Yau 3- fold X the low energy dynamics is that of a black string in 5 dimensional N = 1 supergravity. The infrared dynamics on the string worldsheet is an N = (0, 4) 2D conformal field theory. Assuming the 2D CFT can be described as a nonlinear sigma model, we describe the target space geometry of this mode l in terms of the data of X and P. Variations of weight two Hedge structure s enter the construction of the model in an interesting way.