1991 Fiscal Year Final Research Report Summary
Conformal invariance and superstring theory
| Project/Area Number |
01540237
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SAKAI Norisuke Department of Physics, Tokyo Institute of Technology, Professor, 理学部, 教授 (80108448)
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| Co-Investigator(Kenkyū-buntansha) |
YANG Sung-Kil National Laboratory for High Energy Physics, Associate Professor, 助教授 (70201118)
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| Project Period (FY) |
1989 – 1991
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| Keywords | conformal invariance / supersting theory / operator product expansion / matrix model / two-dimensional gravity / Liouville field / area-preserving diffeomorphism / supersymmetry |
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| Research Abstract |
Superstring Theory is the most promising candidate for a unified theory including gravity. The most basic principle underlying the superstring theory is the conformal invariance in the two-dimensional world sheet. The conformal invariance also plays a crucial role in classifying the second order phase transition in statistical physics in two demensions. Recent progress in matrix models provides a powerful non perturbative treatment of two-dimensional gravity form the viewpoint of discretized theory. Continuum approach based on the Liouville field theory is complementary and particularly useful in revealing physical content.
We have studied the conformal field theory coupled to two-dimensional gravity using the continuum approach. We have succeeded to analyze the partition function and correlation functions in the case of conformal matter with the unit central charge. This case is especially interesting from the viewpoint of string therory, since it allows a space-time interpretalon in the usual sense. We have found that the operator product expansion is very useful in unraveling the singularity structure of the two-dimensional gravity coulpled with the conformal matter. We are also studying the coupling of physical states using the symmetry of area-preserving diffeomorphisms.
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