TY - JOUR

T1 - From loops to states in two-dimensional quantum gravity

AU - Moore, Gregory

AU - Seiberg, Nathan

AU - Staudacher, Matthias

N1 - Funding Information:
The study of two-dimensional random surfaces has many applications. One application is to quantum gravity. Major issues of principle in quantum gravity (e.g. the nature of the Hilbert space and the factorization of amplitudes, measurement theory, the importance of the signature of space-time, etc.) are not understood. The theory of random surfaces is a useful toy model for quantum gravity since, in * This work was supported by DOE grants DE-AC02-76ER03075 and DE-FG05-90ER40559 and by a Presidential Young Investigator Award. ** On leave of absence from the Department of Physics, Weizmann Institute of Science, Rehovot 76100, Israel.

PY - 1991/9/23

Y1 - 1991/9/23

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(91)90548-C

DO - 10.1016/0550-3213(91)90548-C

M3 - Article

AN - SCOPUS:0001032796

SN - 0550-3213

VL - 362

SP - 665

EP - 709

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -