2013-01-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/699133摘要：超弦理論是目前唯一可能可以解釋量子重力等基本物理現象的理論，而我們相信所有的超弦理論被統一在一個假設存在的 M 理論中，所以我們非常希望更瞭解 M 理論。 M 理論中組成物質的基本元素只有兩種： M2 膜及 M5 膜。過去幾年以來，透過對於 BLG 模型及 ABJM 模型的研究，我們對 M2 膜的瞭解已經有了大幅進步，但是 M5 膜仍然令人難以捉摸。此一計畫的目的就是要瞭解關於 M5 膜的物理性質，特別是關於多個 M5 膜重疊在一起的時候的物理描述。過去知道單一個 M5 膜上存在一個自對偶的二階張量規範場，所以我們預期多個 M5 膜重疊在一起的系統中應該要有這種規範理論的非阿貝爾（non-Abelian）推廣。有人建議應該用 twisted non-Abelian 1-gerbes 當作適當的數學架構，但是到目前為止我們仍然缺乏一個具體的物理模型。事實上，如何推廣高階規範場到非阿貝爾的問題是一個老問題，因為這是我們有了高階阿貝爾規範理論之後自然會問的問題。我們希望近年來弦論中的發展可以幫助我們在這個由來已久的重要議題上有值得一提的進展。<br> Abstract: Superstring theories are currently the only candidate for the theory of everything, and all five superstring theories are unified in the M theory, which is so far still a hypothetical theory. It is thus very important to learn more about M theory. M2-branes and M5-branes are the only basic ingredients in M theory. Comparatively, M5-branes are even more mysterious than M2-branes, which became better understood through the study of BLG model and ABJM model in recent years. The purpose of this project is to understand the physical properties of M5-branes, in particular questions related to a system of multiple M5-branes. It is known that there is a self-dual 2-form gauge potential on a single M5-brane, and we expect that there is a non-Abelian generalization of this gauge theory when there are more than one coincident M5-branes. Some conjecture that the suitable mathematical framework is twisted non-Abelian 1-gerbes, but we are still unable to give a concrete description of such a gauge theory. In fact, the question about non-Abelian generalization of n-form gauge theory for n>1 arose long time ago, for it is a natural generalization of the Abelian n-form gauge theory well understood in field theories. We hope that this long-standing problem in field theory can be better understood with the new light shed from string theories.超弦理論Ｍ理論Ｄ膜Ｍ膜代數幾何卡拉比-丘空間superstring theoryM theoryD-braneM-braneAlgebraic GeometryCalabi-Yau space