Moduli Spaces of Fivebranes on Elliptic Calabi-Yau Threefolds

We present a general method for calculating the moduli spaces of fivebranes wrapped on holomorphic curves in elliptically fibered Calabi-Yau threefolds, in particular, in the context of heterotic M theory. The cases of fivebranes wrapped purely on a fiber curve, purely on a curve in the base and, generically, on a curve with components both in the fiber and the base are each discussed in detail. The number of irreducible components of the fivebrane and their properties, such as their intersections and phase transitions in moduli space, follow from the analysis. Even though generic curves have a large number of moduli, we show that there are isolated curves that have no moduli associated with the Calabi-Yau threefold. We present several explicit examples, including cases which correspond to potentially realistic three family models with grand unified gauge group SU(5).