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Generalized dualities relating gravitational theories in 4-dimensional Anti-deSitter space with 3-dimensional conformal field theories

4 维 Anti-deSitter 空间中的引力理论与 3 维共形场论的广义对偶性

基本信息

批准号：
212628803
负责人：
Professor Dr. Olaf Hohm
金额：
--
依托单位：
Institut für Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/212628803?language=en
关键词：
Generalized dualities relating gravitational theories

项目摘要

The Anti-deSitter/Conformal Field Theory (AdS/CFT) correspondence predicts that the number of dimensions is a matter of perspective: we can choose to describe Nature as obeying one set of laws, including gravity, in four dimensions or, equivalently, obeying a different set of laws, excluding gravity, in three dimensions. Despite the radically different descriptions, we have no way to determine which of these dual formulations is “really” true. An analogous phenomenon occurs in everyday life. A hologram is a 2- dimensional object, but it looks like a fully 3-dimensional image. Therefore, the AdS/CFT correspondence is also known as “holography”. Holography in the sense just explained is not just a theoretical curiosity, but has a plethora of applications: a calculation that is very hard in one formulation can be quite simple in a holographically dual picture. For instance, AdS/CFT allows to map the physics of certain black holes to the physics of strongly coupled field theories, and vice versa. The main goal of this project is to establish and study generalized dualities between non-standard theories of gravity in AdS, like higher derivative theories and/or theories with higher spin, and specific CFTs. Such a correspondence may have applications, e.g., in condensed matter physics to describe strongly coupled systems with quenched disorder by means of a gravity theory dual to a log CFT. Applying the correspondence in the other direction may lead to new insights into 4-dimensional quantum gravity in AdS by studying its dual CFT.

反偏移场/共形场理论(ADS/CFT)的对应预言了维度的数量是一个视角问题：我们可以选择将自然描述为在四个维度遵守一组定律，包括引力，或者等价地，在三个维度遵守一组不同的定律，不包括重力。尽管有截然不同的描述，但我们无法确定这些双重配方中哪一种是“真正”正确的。类似的现象在日常生活中也会发生。全息图是一个2维的物体，但它看起来像一个完全的3维图像。因此，ADS/CFT通信也被称为“全息照相”。刚才解释的意义上的全息术不仅是理论上的好奇，而且有太多的应用：在一个公式中非常困难的计算在全息双重图像中可以非常简单。例如，ADS/CFT允许将某些黑洞的物理映射到强耦合场论的物理，反之亦然。这个项目的主要目标是建立和研究ADS中的非标准引力理论之间的广义对偶，如高阶导数理论和/或具有更高自旋的理论，以及具体的CFT。这样的对应关系可以应用于例如凝聚态物理中，借助于对数CFT的双重引力理论来描述具有猝灭无序的强耦合系统。将对应关系应用到另一个方向，可能会通过研究ADS中的对偶CFT来对ADS中的四维量子引力有新的见解。