Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory Original Research Article

We consider compactifications of the N = 1, d = 6, E8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2,Z) duality of the N = 2, d = 4, SU(2) theory with Nf = 4. Using this theory on a D-brane probe we shed new light on the singularities of F-theory compactifications to eight dimensions. As another application we consider compactifications of F-theory, M-theory and the IIA string on (singular) Calabi-Yau spaces where our theory appears in space-time. Our viewpoint leads to a new perspective on the nature of the singularities in the moduli space and their space-time interpretations. In particular, we have a universal understanding of how the singularities in the classical moduli space of Calabi-Yau spaces are modified by world-sheet instantons to singularities in the moduli space of the corresponding conformal field theories.