Heterotic M – Theory Vacua with Five – Branes ∗

We construct vacua of heterotic M–theory with general gauge bundles and five–branes. Some aspects of the resulting low–energy effective theories are discussed. M–theory on the orbifold S/Z2 is believed to describe the strong coupling limit of the E8 × E8 heterotic string [1] and, therefore, constitutes a particularly interesting starting point for M–theory particle phenomenology. At low energy, this theory is described by 11–dimensional supergravity coupled to two 10–dimensional E8 gauge multiplets residing on the two fixed points of the orbifold [2, 4, 3]. Compactifications leading to N = 1 supersymmetry in four dimensions are based on space–times of the structure M11 = S /Z2 ×X ×M4, (1) where X is a Calabi–Yau three-fold and M4 is flat Minkowski space. While most work to date, related to such compactifications of heterotic M–theory, has been limited to the standard embedding, non–standard embedding vacua have previously been addressed in [6, 7, 8]. Here, we will consider the general configuration leading to N = 1 supersymmetry [9], where, first, we allow for general gauge bundles, and, second, include five-branes [3], states which are essentially non-perturbative in heterotic string theory. The important new ingredient is the presence of these five–branes in the vacua. Some effects caused by the presence of the five–branes have been discussed in [7, 10]. Due to gauge and gravity sources on the orbifold planes and the five–brane sources, the space–time (1) receives corrections that can be computed perturbatively as an expansion in [5] ǫS = ( κ 4π )2/3 2πρ v2/3 , (2) where κ, v and ρ are the 11–dimensional Newton constant, the Calabi–Yau volume and the orbifold radius, respectively. Talk presented by A. Lukas at the 32nd Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, September 1 5, 1998