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A Large N Type IIB Duality via a Spin(7) Geometric Transition as an F-theory Flop | | M.C. Tan
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20 Sep 2004 | | Subject: | hep-th | | 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 $it dual$ geometry with no branes but with certain units of 3-form fluxes through appropriate 3-cycles. For small $it{or}$ 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, $spin^c$ manifold undergoing the $it{smooth}$ $mathbb {RP}^5$ 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. | | Source: | arXiv, hep-th/0409196 | | Services: | Forum | Review | PDF | Favorites | |
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