2004/09/20 by M. C. Tan, Tan, M. C.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0409196
62 pages, 2 figures, LaTeX. Major conceptual changes from v1 and v2
arxiv created 2005/06/19 · arxiv updated 2009/12/01
The geometric features and toric descriptions of two different 8-dimensional Spin(7) manifolds constructed via distinct resolutions of the cone over an SU(3)/U(1) base, reveals that the geometry of the Spin(7) conifold transition considered by Gukov et al. in \citegst, is effected by a transition in its 6-dimensional submanifold which is isomorphic to a resolved or deformed Calabi-Yau 3-fold. This allows for a natural extension of the Gopakumar-Vafa large N superstring duality of \citegv, v; IIB superstring theory compactified on the Spin(7) manifold with N space-filling D5-branes wrapping an even-dimensional supersymmetric cycle, can be argued to undergo a large N geometric transition at low energy to a \it dual geometry with no branes but with certain units of 3-form fluxes through appropriate 3-cycles. For small \itor large string coupling in a non-trivial axion field background, this large N type IIB duality can be lifted to a purely geometric \mathbb RP5 flop without D5-branes and 3-form fluxes via an F-theoretic description. The orientable, 10-dimensional, non-compact, Ricci-flat, spinc manifold undergoing the \itsmooth \mathbb RP5 flop possesses an extended SU(5) \odot \mathbb Z2 holonomy group, thus preserving 1/32 of the maximal supersymmetry, consistent with the resulting \mathcal N =(1,0) supersymmetric pure SU(N) theory in 1+1 dimensions.