Little Theories in Six and Seven Dimensions

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We discuss theories with 16 and 8 supercharges in 6 and 7 dimensions. These theories are defined as world-volume theories of 5- and 6-branes of type II and M theories, in the limit in which bulk modes decouple. We analyze in detail the spectrum of BPS extended objects of these theories, and show that the 6 dimensional ones can be interpreted as little (non-critical) string theories. The little 5-branes of the 6 dimensional theories with 16 supercharges are used to find new string theories with 8 supercharges, which have additional group structure. We describe the web of dualities relating all these theories. We show that the theories with 16 supercharges can be used for a Matrix description of M-theory on T⁶ in the general case, and that they also reproduce Matrix theory on T⁵ and T⁴ in some particular limit.