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On c=1 matrix model and 2D gravity - with emphasis on chiral formalism Wang, Daoyan


In this thesis, we study the relationship between the effective spacetime theory of Liouville string theory in two spacetime dimensions and the collective field of the c=1 matrix model by finding exact solutions on both sides. The correspondence between the matrix model and the effective spacetime theory turns out to be nonlinear in their fields. By comparing the exact solutions on both side, we show the nonlinearity begins to appear at the second order in terms of the incoming tachyon field. In particular, we employ the chiral formalism in the matrix model the formalism allowing to write down solutions to equations of motion explicitly — to find out exact solutions. We show the chiral formalism is much simpler than the more traditional classical field method. Also it is more powerful as it enables us to study the behavior around the singular point in the background of the matrix model.

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