String Theory Journal Club

I will overview the "microscopic" bosonization approach to the evaluation of correlation functions in one-dimensional quantum fluids. The essence of this method lies in exact accounting for the soft-mode excitations around the vacuum state. I will try to explain how this is related to conformal field theory, Riemann-Hilbert problem, Painleve equations, Integrable systems, etc. My main example will be a Fredholm determinant of the sine kernel, which is also nicely connected to the Hermitian Matrix Models. Finally, if time permits, I will explain how to generalize this machinery for the computation of correlation functions on the finite entropy state.