本研究計畫主題為``多分割矩陣模型與非臨界弦理論(Multi-cut Matrix Models and Non-critical String Theory)’’。本計畫預計研究的重點有二： (1) 如何將非臨界弦論(non-critical string theory)嵌入(embed)具適當時空背景場的臨界弦論，進而利用矩陣模型的工具了解臨界弦論(critical string theory)的非微擾物理及其對稱原理。 (2) 透過在矩陣模型中矩陣特徵值複數平面上分割(branch cut)的調控，我們可以找到非臨界弦論中玻色(bosonic)與超對稱(supersymmetric)的連續場論。更進一步，如果我們研究多重分割(multi-cut)的矩陣模型，我們希望在非臨界弦論中尋找對應到新的對稱及連續場論。 The title of this research project is Multi-cut Matrix Models and Non-critical String Theory. We hope to focus on the following two subjects: (1) We hope to find appropriate embeddings of the non-critical string theory into the critical string theory with certain space-time background fields. Then one can rely on the tools of matrix model to understand the symmetry principles and non-perturbative properties of the critical string theory. (2) By suitable adjustments of the branch-cut structures of the complex plane associated with matrix eigen-values, we can identify the corresponding bosonic (one-cut) and supersymmetric (two-cut) Liouville string theory. We wish to explore the multi-cut generalizations and ask what is the corresponding symmetry and Liouville string theory.
