The Universal Geometry of Heterotic Vacua

This talk is about derivatives and gauge symmetries. We describe how a study of derivatives and gauge symmetries on the moduli space of N=1 d=4 heterotic vacua leads to a generalised "universal bundle". The resulting geometry unifies tensors for the heterotic theory with tensors on the moduli space. Deformation theory, replete with all its complicated algebraic relations, is recast in terms of simple tensor equations. The surprising fact is that this is a useful thing to do.