A Large N Type IIB Duality via a Spin(7) Geometric Transition as an F-theory Flop

Abstract

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 \cite{gst}, 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 \cite{gv, 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 $dual$ geometry with no branes but with certain units of 3-form fluxes through appropriate 3-cycles. For small $or$ large string coupling in a non-trivial axion field background, this large $N$ type IIB duality can be lifted to a purely geometric ${\mathbb{RP}}^5$ flop without D5-branes and 3-form fluxes via an F-theoretic description. The orientable, 10-dimensional, non-compact, Ricci-flat, $spi{n}^c$ manifold undergoing the $smooth$ ${\mathbb{RP}}^5$ flop possesses an extended $SU(5)\odot {\mathbb{Z}}_2$ 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.

arXiv comment62 pages, 2 figures, LaTeX. Major conceptual changes from v1 and v2

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