Abstract
Two-dimensional quantum gravity is relevant both for string theory and as a toy model of higher-dimensional quantum gravity. The definition of pure 2D quantum gravity and quantum gravity coupled to matter in terms of matrix models1 is very explicit and rigorous. Matrix realizations of pure gravity and gravity coupled to certain minimal conformai field theories (and their massive deformations) can be solved by the application of large-N techniques. Recently, an exact expression for the specific heat of some of these models was found in the continuum limit.2-6 In this chapter, we will show that the correlation functions of operators in these models can also be easily computed. We distinguish between two kinds of operators, microscopic and macroscopic loops. By microscopic loops we mean expressions like Tr M p in the matrix models with p finite. They contain all the information about integrals over the surface of local operators.
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We thank L. Susskind for discussions of this point.
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Banks, T., Douglas, M.R., Seiberg, N., Shenker, S.H. (1992). Microscopic and Macroscopic Loops in Nonperturbative Two-Dimensional Gravity. In: Teitelboim, C., Zanelli, J. (eds) Quantum Mechanics of Fundamental Systems 3. Series of the Centro de Estudios CientÃficos de Santiago. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3374-0_2
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