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Bobby Acharya : M Theory, G_2 Holonomy spaces and N=1 Theories in Four Dimensions

After reviewing some reasons why one might be interested in G_2 holonomy compactifications of M theory, I shall review some of the recent results about such vacua, which are mainly due to Atiyah, Maldacena, Vafa, Witten, and myself in various collaborations. Topics covered will mainly center around how various aspects of super Yang-Mills theory can be related to properties of M theory in such spacetime backgrounds. These will include instantons, domain walls and confinement.

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