Nonabelian structures on D-branes and M-branes

该提案的共同主题是弦论和M理论中膜上的非交换和非对易现象。弦理论的一个显著特征是当几个D-膜重合时出现非交换结构。这些非交换结构在D膜物理中起着重要的作用。它们也与普通量子场论的新见解有关。单个D-膜的动力学完全由阿贝尔规范场通过Born-Infeld作用量描述。一个完整的nonabel推广这个行动尚未发现。相当复杂的方法已被用来找到所有的条款，直到四阶0。我们提出了一个系统的方法来理解的一般结构的nonabelian玻恩-因菲尔德行动的基础上，我们已经开发的非对易规范理论的方法。作为第一步，我们将研究非交换的Seiberg-Witten映射，一个从普通的杨-米尔斯场到非对易规范场的映射。这一部分的研究主要是针对D膜的非交换性现象。这是很好理解的情况下，只有在拓扑平凡的背景，但很少知道在更一般的背景。弦激发的非对易性的想法在传统的量子场论中也被证明是非常有用的，它产生了新的现实的无异常（有效）粒子模型，可以想象在下一代粒子加速器的实验中进行测试。对非对易现象及其场论意义的进一步理解是非常必要的。它也可以提供一个概念框架，让我们理解在大多数一般背景下，哪种数学与描述弦场论最相关。另一个关于非阿贝尔结构的有趣问题，发生在我们考虑弦论中在高阶规范场下带电的高维物体时。阿贝尔规范理论可以推广到格贝斯和斯塔克框架下的高阶势理论。然而，对于非阿贝尔形式，没有这样的推广。这个项目的一部分是关于这个问题的，它涉及到非平凡H场中D-膜的非对易描述及其使用非对易格贝的低能有效作用，以及使用（对易）非交换格贝描述M5-膜（或NS 5-膜）物理。一个相关的问题是在不同的开弦背景下一般开弦场论的“森田等价”。

The common theme of the proposal are nonabelian and noncommutative phenomena on branes in string theory and M-theory. A remarkable feature of string theory is the appearance of nonabelian structures when several D-branes coincide. These nonabelian structures play an important role in D-brane physics. They are also related to new insights in ordinary Quantum field theory. The dynamics of a single D-brane is completely described by abelian gauge fields via the Born-Infeld action. A full nonabelian generalization of this action has not yet been found. Quite sophisticated methods have been used to find all terms up to fourth order in 0. We propose a systematic approach to an understanding of the general structure of the nonabelian Born-Infeld action based on methods that we have developed for noncommutative gauge theory. As a preliminary step we shall study the nonabelian Seiberg-Witten map, a map from ordinary Yang-Mills fields to noncommutative gauge fields. This part of the proposed research is devoted to phenomena of non-commutativity of Dbranes. This is well understood only in the case of topologically trivial backgrounds but very little is know in the case of more general background. The idea of stringy inspired non-commutativity proved to be very useful also in the traditional quantum field theory where it produced new realistic anomaly free (e ective) particle models that can conceivably be tested in experiments on the next generation of particle accelerators. Further understanding of the non-commutativity phenomena and its field theoretical implications is highly desirable. It could give as also the conceptual framework of understanding what kind of mathematics is the most relevant to describe String Field Theory in most general backgrounds. Another interesting problem concerning nonabelian structures occurs when we consider higher-dimensional objects in string theory that are charged under higherform gauge fields. Abelian gauge theories can be generalized to theories with higherform potential in the framework of gerbes and stacks. No such generalization is, however, known for nonabelian forms. The part of this project that is concerned with that problem is related to the noncommutative description of D-branes in a nontrivial H-field and their low energy e ective actions using noncommutative gerbes and to the description of M5-branes (or NS 5-brane) physics using (commutative) nonabelian gerbes. A related question is the "Morita equivalence" of general open string field theories in di erent open string backgrounds.