From loops to states in two-dimensional quantum gravity

Gregory Moore, Nathan Seiberg, Matthias Staudacher

Research output: Contribution to journalArticlepeer-review

204 Scopus citations


We investigate macroscopic loop amplitudes (at genus zero) using the matrix model and the Liouville theories of two-dimensional quantum gravity. Some loop amplitudes, interpreted as wave functions of local operators, satisfy a linear differential equation known as the Wheeler-deWitt equation. Moreover, from the properties of the loop amplitudes an inner-product space structure on the space of wave functions emerges naturally. In the course of our analysis we resolve several apparent discrepancies between the matrix model and Liouville theory. Macroscopic loops provide a natural ultraviolet cutoff on the theory, rendering universal analytic terms in the coupling constants. They contain more information than the local operators and should be regarded as fundamental.

Original languageEnglish (US)
Pages (from-to)665-709
Number of pages45
JournalNuclear Physics, Section B
Issue number3
StatePublished - Sep 23 1991

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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