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An M-theory flop as a large $$N$$ duality. (English) Zbl 1061.81056
Summary: We show how a recently proposed large $$N$$ duality in the context of type IIA strings with $$\mathcal N = 1$$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $$G_2$$ holonomy manifolds and an $$S_3$$ flop are the key ingredients in this derivation.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 53C29 Issues of holonomy in differential geometry 83E30 String and superstring theories in gravitational theory
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