1990 Fiscal Year Final Research Report Summary
Conformal Supergravity and String Model
| Project/Area Number |
63540216
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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 | Kyoto University |
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Principal Investigator |
UEMATSU Tsuneo Kyoto University, College of Liberal Arts & Sciences, Associate Professor, 教養部, 助教授 (80093194)
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| Project Period (FY) |
1988 – 1990
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| Keywords | Superconformal / Supergravity / Superspace / Sine-Gordon / Conservation / Perturbation / Superstring / Soliton |
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| Research Abstract |
It has been widely known that the string model is the most promising candidate for the unified theory of all fundamental interactions including gravity. This model is characterized by the superconformal symmetry in the two-dimensional world sheet drawn by strings in space-time. The conformal supergravity is the gauge theory of this symmetry. Recently, there has been much interest in studying the superconformal algebras in the context of the compactification of strings and the critical phenomena in two-dimensional statistical systems. In the first year of the present research project, we obtained the superspace formulation of N=4 superconformal algebras. We constructed the screening operators which play the important role for the representation theory. In the second year, we calculated the super Schwarzian derivative that represents the anomalies of finite transformations and is important in the study of super Riemann surfaces. In the last year, we investigated off-critical behaviors of superconformal field theories. We extended N=0 sine Gordon theory as a perturbed system to the N=1 and N=2 supersymmetric cases. We obtained quantum conserved charges of vertex oparator type in addition to the ordinary conserved charges of polynomials in super-Virasoro operators. We studied conservation laws at the classical level as well as at the quantum level based on the perturbation theory for N=1 and N=2 sine-Gordon theories. In superstring theory, the space-time N=1 supersymmetry leads to the N=2 world-sheet symmetry. In this respect, N=2 soliton theories attract much interest. The existence of extra charges of vertex operator type are closely related to the structures of S matrices. During the course of research, the discussions with the people at University of Tokyo and KEK and so on were of great help. We published what we obtained in the present research in the journals and presented the results at several workshops, JPS meetings and seminars in various institues.
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