Nonabelian structures on D-branes and M-branes

该建议的共同主题是弦理论和m理论中膜上的非abel和非交换现象。弦理论的一个显著特征是当几个d膜重合时出现非阿贝尔结构。这些非abel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。通过玻恩-因菲尔德作用，用阿贝尔规范场完全描述了单个d膜的动力学。这个作用的完整的非abel泛化还没有被发现。相当复杂的方法已经被用来求出0的所有四阶项。我们提出了一种系统的方法来理解非abel Born-Infeld作用的一般结构，该方法基于我们为非交换规范理论开发的方法。作为初步的步骤，我们将研究非abel Seiberg-Witten映射，一个从普通Yang-Mills场到非交换规范场的映射。这一部分研究的是膜的非交换性现象。这只有在拓扑琐碎的背景下才能很好地理解，但在更一般的背景下却知之甚少。弦激发的非交换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。进一步了解非交换性现象及其场理论意义是非常可取的。它也可以提供一个概念性的框架来理解在大多数的背景下，什么样的数学最适合描述弦场论。另一个关于非阿贝尔结构的有趣问题出现在我们考虑弦理论中的高维物体时，这些物体在高形式规范场下带电。阿贝尔规范理论可以推广到gerbes和堆栈框架下具有更高性能势的理论。然而，对于非贝尔形式，没有这样的推广。本项目中与该问题有关的部分涉及到非平凡h场中d膜的非交换描述及其使用非交换gerbes的低能有效作用，以及使用（交换）非abel gerbes描述m5膜（或ns5膜）物理。一个相关的问题是，在不同开放弦背景下，一般开放弦场论的“森田等价”问题。

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.