String Theory and Statistical Many-body Systems

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In this research project, we studied using field theoretical techniques the intimatelyelated structures of string theory and statistical many-body system at criticality and obtained the following results :1. String theories can be considered as conformally invariant field theories (CFT's) on the string world sheet. A promising framework capable of describing various CFT's comprehensively is the free-field realization introduced by Feigin and Fuchs. We have succeeded in constructing such realizations for the su (n) Kac-Moody algebras and the associated parafermionic systems which are of fundamental importance.2. To clarify the relations among various string theories, it is important to study the whole set of two dimensional field theories including gravitational degree of freedom. Recently the exact solution of two dimensional quantum gravity has been obtained by the matrix model approach and moreover the same results can be reproduced by the method of topological field theories (TFT's) which are conceptually quite distinct. We have proposed a formulation of TFT's possessing conformal symmetry and found novel closed algebraic structures of interest.3. Anti-ferromagnetic (AF) long range order is considered a key concept in unraveling the high TALL_c superconductivity. We have shown that the OMICRON (3) non-linear sigma model provides the effective description of the long-distance behavior of the AF Heisenberg model and analyzed it field theoretically. Weak dependence on the three dimensionality has also been studied.4. Doped high TALL_c superconductor can be described by the t-J model. We analyzed its effective theory, the RHO^1 model, and obtained results on the phase structure, transition temperature, etc., which are in good agreement with experiments. We also found the occurrence of hole-pair condensation and proposed that this serves as the main mechanism of high TALL_c superconductivity.