M-Theory Dynamics On A Manifold Of G₂ Holonomy

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We analyze the dynamics of M-theory on a manifold of G₂ holonomy that is developing a conical singularity. The known cases involve a cone on CP³, where we argue that the dynamics involves restoration of a global symmetry, SU(3)/U(1)², where we argue that there are phase transitions among three possible branches corresponding to three classical spacetimes, and S³ x S³ and its quotients, where we recover and extend previous results about smooth continuations between different spacetimes and relations to four-dimensional gauge theory.