Non-perturbative Phenomena and Background (In)dependence in Field and String Theory

场论和弦论中的非微扰现象和背景（独立）依赖性

• 批准号: 184125276
• 负责人: Dr. Murad Alim
• 金额: --
• 依托单位: Department of Physics
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/184125276?language=en
• 关键词: Non; perturbative; Phenomena; Background; dependence

Field theories describe a broad range of physical phenomena. Many field theories exhibit dualities which exchange strong and weak coupling together with an exchange of fundamental and non-perturbative degrees of freedom. Understanding dualities has led to a great leap forward for both field and string theories which furthermore incorporate the coupling to gravity. Within string theory, a geometrical meaning can be given to dual formulations of the same theory. Furthermore it is possible to scrutinize the dependence of the theory on its couplings and parameters, i.e. its background dependence. The gained insights allow exact computations of physical quantities. Moreover addressing the question of background dependence has led to intriguing new insights allowing to connect and rethink some of the most fundamental physical notions. The goal of this research program is to extend and deepen the understanding of background dependence of string theories and the possibility to give a background independent meaning to physical quantities. The focus hereby is on phenomena which are related to the perturbative loop expansion of string theory which is governed by the string coupling constant. Non-perturbative effects with respect to this coupling are the D-branes, which are the boundary conditions of string theory. This expansion moreover corresponds to coupling field theories to gravity. Prospects of this research for four-dimensional physical theories are to obtain a precise handle on the effective couplings of physical theories engineered by D-brane setups and to obtain insights into an effective theory of quantum gravity. Furthermore, insights into the non-perturbative completion and S-duality of string theory are expected. On the mathematical side these very concepts are subject of research in the field of mirror symmetry where physical dualities are translated into surprising relations of different areas in mathematics and allow to compute mathematical invariants.

场论描述了广泛的物理现象。许多场论表现出交换强耦合和弱耦合以及交换基本自由度和非摄动自由度的对偶性。对偶性的理解使场理论和弦理论都有了很大的飞跃，它们进一步将引力的耦合结合起来。在弦理论中，同一理论的对偶表述可以赋予几何意义。此外，有可能仔细检查理论对其耦合和参数的依赖性，即其背景依赖性。获得的见解使物理量的精确计算成为可能。此外，对背景依赖性问题的解决带来了有趣的新见解，使我们能够将一些最基本的物理概念联系起来并重新思考。本研究计划的目标是扩展和加深对弦理论背景依赖性的理解，以及赋予物理量背景独立意义的可能性。本文的重点是与弦理论中受弦耦合常数控制的微扰环展开有关的现象。关于这种耦合的非扰动效应是d膜，它是弦理论的边界条件。而且，这种扩展与引力耦合场论相对应。四维物理理论研究的前景是精确地处理由d膜装置设计的物理理论的有效耦合，并获得对量子引力有效理论的见解。此外，对弦理论的非微扰完备性和s -对偶性也有深入的了解。在数学方面，这些概念是镜像对称领域的研究主题，其中物理对偶性被转化为数学中不同领域的惊人关系，并允许计算数学不变量。