A Membrane theory

what are the main concepts of membrane theory? the most beautiful possible giresults.

g → 1/g where g is the coupling constant
ive read that this transformation changes a dirichlet membrane into fundamental strings. does this have something to do with evaporation of black holes?
 
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theory of topological defects. solitons, black holes, magnetic monopoles and dirichlet membranes are essentially the same?
 
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g → 1/g where g is the coupling constant
ive read that this transformation changes a dirichlet membrane into fundamental strings. does this have something to do with evaporation of black holes?
That's a duality between strong and weak coupling. It's called S-duality if it is in string theory, or in a field theory that derives from string theory. From memory, the SO(32) heterotic string is S-dual to the D1-brane of Type I string theory; but that's just how it works in that particular case.
theory of topological defects. solitons, black holes, magnetic monopoles and dirichlet membranes are essentially the same?
In general, they are not the same; but there are black branes which I suppose have all those properties at once.

Much of the field theory of duality is covered in "Electromagnetic duality for children". As for string theory, one should be interested in the web of dualities among the various string theories, and then how these sometimes explain the field-theory dualities. It is a big topic, but you could look for monopole papers by Ashoke Sen from early 1990s as a starting point.
 

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