Boundaries and boundary operators in one and two matrix models.

Jean-Emile Bourgine

Seoul

Mon, Dec. 20th 2010, 11:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

The hermitian matrix model is known to reproduce in the continuum limit the (2,2p+1) Minimal Liouville Gravity (MLG). Recently, new matrix boundaries were introduced, reproducing any boundary conditions of the MLG. This construction can be seen as a consequence of a linear relation among the boundary states (FZZT branes). The identification of the boundaries is done at the level of the disc partition function, and one and two point disc correlators. Once the boundaries are identified, we can also consider the insertion of boundary operators. Those will be explicitly constructed for the disc boundary 2-pt function. \par The previous boundary construction can be extended to the two matrix model which leads in the continuum limit to the general (p,q) MLG. In this context, the realization of several symmetries among FZZT branes will be discussed.

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