[en] A conjecture relating instanton calculus in four dimensional supersymmetric theories and the deformation theory of Lagrangian submanifolds in C2r invariant under a (subgroup of) Sp(2r,Z) is formulated. This is a four dimensional counterpart of the mirror symmetry of topological strings (relating Gromov-Witten invariants and generalized variations of Hodge structure). (orig.)
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[en] 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 model in terms of the data of X and P. Variations of weight two Hodge structures enter the construction of the model in an interesting way. (orig.)
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