Flux, Gaugino Condensation and Anti-Branes in Heterotic M-theory James Gray1, Andr´eLukas2 and Burt Ovrut3 1Institut d’Astrophysique de Paris and APC, Universit´ede Paris 7, 98 bis, Bd. Arago 75014, Paris, France 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK 3Department of Physics, University of Pennsylvania, Philadelphia, PA 19104–6395, USA Abstract We present the potential energy due to flux and gaugino condensation in heterotic M- theory compactifications with anti-branes in the vacuum. For reasons which we explain in detail, the contributions to the potential due to flux are not modified from those in supersymmetric contexts. The discussion of gaugino condensation is, however, changed by the presence of anti-branes. We show how a careful microscopic analysis of the system allows us to use standard results in supersymmetric gauge theory in describing such effects - despite arXiv:0709.2914v1 [hep-th] 18 Sep 2007 the explicit supersymmetry breaking which is present. Not surprisingly, the significant effect of anti-branes on the threshold corrections to the gauge kinetic functions greatly alters the potential energy terms arising from gaugino condensation. 1email:
[email protected] 2email:
[email protected] 3email:
[email protected] 1 Introduction In [1], the perturbative four-dimensional effective action of heterotic M-theory compactified on vacua containing both branes and anti-branes in the bulk space was derived. That paper concentrated specif- ically on those aspects of the perturbative low energy theory which are induced by the inclusion of anti-branes. Hence, for clarity of presentation, the effect of background G-flux on the effective theory was not discussed.