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While surfing through some further reading suggestions on string theory, I stumbled upon this slide from a talk by Nathan Seiberg. I wanted to derive the main argument by applying a perturbation expansion for this partition function, but I couldn't get my head around the concept of a phase space for N by N matrices. I am accustomed to the techniques of path integrals in QFT, but for this case I couldn't even move my pen. How can I learn more about matrix models and partition functions for matrices so that I can show that simple matrix models have a stringy perturbation expansion?
It says that it looks like a string theory because string theory has an expansion in term of surfaces that has a similar power counting (replace $$N^2$$ with $$g_s$$). If you take the two index from the matrix like index in a gauge model, you can make the diagrams organize in a way similar to the large N expansion in gauge theories, like planar diagrams, genus-1 diagrams, etc., that has the same power counting-surface topology structure that string theory (there are people that says that eventually gauge theories will be strings because of this, I think they are seeing more than what there is). Also, some Matrix models end up reproducing type IIA and type IIB theories.
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