Calabi–Yau Black Holes and (0,4) Sigma Models

Abstract:

When an M-theory fivebrane wraps a holomorphic surface ? in a Calabi–Yau 3-fold X the low energy dynamics is that of a black string in 5 dimensional ? =1 supergravity. The infrared dynamics on the string worldsheet is an ? = (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 model in terms of the data of X and ?. Variations of weight two Hodge structures enter the construction of the model in an interesting way.