Heterotic Kink Solitons and their Worldvolume Action

We present a formalism for computing the higher-order corrections to the worldvolume action of a co-dimension one kink soliton embedded in five-dimensional heterotic M-theory. The geometry of heterotic M-theory, as well as the effective theory which describes a five-brane wrapping a holomorphic curve by a topological kink in a scalar field, is reviewed. Using this formalism, the explicit worldvolume action is computed to second order in two expansion parameters--one describing the "warp" of the heterotic geometry and the second the fluctuation length of the soliton hypersurface. The result is expressed in terms of the trace of the extrinsic curvature and the intrinsic curvature scalar.