February 1, 2008 hep-th/0207244 MIT-CTP-3284 HUTP-02/A014 DAMTP-2002-85 Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds Sergei Gukov1, James Sparks2, and David Tong3 1Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A.
[email protected] 2Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
[email protected] 3Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
[email protected] arXiv:hep-th/0207244v2 16 Sep 2002 Abstract We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first non- trivial example of a topology changing transition with only 1/16 supersymmetry. Contents 1 Introduction 1 2 D6-Branes, M-Theory and Spin(7) Conifolds 7 2.1 D6-Branes and the Cone over SO(5)/SO(3) ............... 8 2.2 D6-Branes and the Cone over SU(3)/U(1) ................ 10 2.3 DeformationsofCoassociativeCones . ... 12 2.4 AnomaliesandSupersymmetry .