Non-perturbative vacua and particle physics in M-theory

In this letter, we introduce a general theory for the construction of parti cle physics theories, with three families and realistic gauge groups, withi n the context of heterotic M-theory. This is achieved using semi-stable hol omorphic gauge bundles over elliptically fibered Calabi-Yau three-folds. Co nstruction of realistic theories is facilitated by the appearance of non-pe rturbative five-branes in the vacuum. The complete moduli space of these fi ve-branes is computed and their worldvolume gauge theory discussed. In the context of holomorphic gauge bundles, it is shown how grand unified gauge g roups can be spontaneously broken to the gauge group of the standard model. These ideas are illustrated in an explicit SU(5) three-family example.