Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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40 pages, 2 figures, harvmac with epsf. Minor corrections, references added

Scientific paper

10.1016/S0550-3213(96)00690-6

We consider compactifications of the N=1, d=6, E_8 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,\IZ) duality of the N=2, d=4, SU(2) theory with N_f=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 spacetime. Our viewpoint leads to a new perspective on the nature of the singularities in the moduli space and their spacetime interpretations. In particular, we have a universal understanding of how the singularities in the classical moduli space of Calabi--Yau spaces are modified by worldsheet instantons to singularities in the moduli space of the corresponding conformal field theories.

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