Boundary Liouville Theory and 2D Quantum Gravity

Details Boundary Liouville Theory and 2D Quantum Gravity Boundary Liouville Theory and 2D Quantum Gravity

2003-07-20

arxiv.org/abs/hep-th/0307189v3

Nucl.Phys. B683 (2004) 309-362

Physics

High Energy Physics

High Energy Physics - Theory

52 pages, 21 figures. Substantial revision. A new chapter added

Scientific paper

10.1016/j.nuclphysb.2004.02.009

We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the one obtained for the boundary two-point function by Fateev, Zamolodchikov and Zamolodchikov. All these functional identities can be written as difference equations with respect to one of the boundary parameters. Then we switch to the microscopic realization of 2D quantum gravity as a height model on a dynamically triangulated disc and consider the boundary correlation functions of electric, magnetic and twist operators. By cutting open the sum over surfaces along a domain wall, we derive difference equations identical to those obtained in Liouville theory. We conclude that there is a complete agreement between the predictions of Liouville theory and the discrete approach.

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