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Notes on Quantum Liouville Theory and Quantum Gravity
Abstract
There are two motivations to study two-dimensional quantum gravity. First, this theory is a toy model for four-dimensional gravity. Second, two-dimensional quantum gravity is the theory on the world-sheet of both “critical” as well as “non-critical” string theories. Some of our conclusions apply to these two more general situations. Since we would like to draw lessons from this simple theory, which are generic and valid in more complicated systems, we should study it in continuum field theory language. In these notes we review the status of the continuum Liouville approach to quantum gravity. Our understanding of the subject is far from complete. We will point out what we think are the most important open problems, and will speculate about their solutions.
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Citations
Cites
Strings in less than one dimension
Douglas, M. R., & Shenker, S. H. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90522-f · Cited by 1,103
Diseases of triangulated random surface models, and possible cures
Ambjørn, J., Durhuus, B., & Fröhlich, J. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90356-6 · Cited by 645
Cited by
Quantum gravity: a progress report
Carlip, S. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/8/301 · Cited by 449
JT gravity as a matrix integral
Saad, P., Shenker, S. H., & Stanford, D. (2019) · arXiv · doi:10.48550/arxiv.1903.11115 · Cited by 442
Linear dilatons, NS5-branes and holography
Aharony, O., Berkooz, M., Seiberg, N., & Kutasov, D. (1998) · Journal of High Energy Physics · doi:10.1088/1126-6708/1998/10/004 · Cited by 390
Self-citationLIOUVILLE FIELD THEORY: A DECADE AFTER THE REVOLUTION
NAKAYAMA, Y. (2004) · International Journal of Modern Physics A · doi:10.1142/s0217751x04019500 · Cited by 371
Strings from tachyons: the c= 1 matrix reloaded
McGreevy, J., & Verlinde, H. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/12/054 · Cited by 300
Metadata
- Authors
- Seiberg, N.
- Venue
- Progress of Theoretical Physics Supplement
- Publisher
- Oxford University Press (OUP)
- Published
- 1990
- Volume
- 102
- Pages
- 319-349
- ISSN
- 0375-9687 (ISSN-L)
- OpenAlex
- W2143030161
- Cited by
- 572
- References
- 2
- FWCI
- 23.54
- Type
- journal article
- Language
- en
- Open access
- closed
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