One- and two-matrix models and random cylindre with two-coloured boundaries

Details One- and two-matrix models and random cylindre with two-coloured boundaries One- and two-matrix models and random cylindre with two-coloured boundaries

2004-11-04

arxiv.org/abs/hep-th/0411054v1

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 9 figures, LaTex, report in french

Scientific paper

In this training course report, I briefly present the one- and two-matrix models as tools for the study of conformal field theories with boundaries. In a first part, after a short historical presentation of random matrices, I present the matrix models' formalism, their diagramatic interpretation, their link with random surfaces and conformal field theories and the "loop equations" method for the 2-matrix model. In a second part, I use this method for the calculation of the generating function of random cylindres whose boundaries are two-coloured, which was not know before.

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