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Chapter 12 of Beckers' book about superstrings and m-theory lists several deep dualities between low energy gauge theories and high energy superstring theories. I am only at the Chapter 2, that is why I have my question: what is analogue to the nonrelativistic low energy quantum wave function in the gauge theories and superstring theories. I guess that gauge theories and superstring theories admits such analogues for the particles, fields, superstrings, branes and for the ensembles of those creatures. And I guess that those analogues more or less smoothly transforms into wave functions in the infrared limit. So, what are those analogues?

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