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

反deSitter/共形场论（AdS/CFT）对应预言，维度的数量是一个视角问题：我们可以选择在四维中将自然描述为遵守一组定律，包括引力，或者等价地，在三维中遵守一组不同的定律，不包括引力。尽管有着截然不同的描述，但我们无法确定这些对偶公式中哪一个是“真正”正确的。类似的现象也发生在日常生活中。全息图是一个二维物体，但它看起来像一个完全三维的图像。因此，AdS/CFT对应也被称为“全息术”。在刚才解释的意义上，全息术不仅仅是一种理论上的好奇心，而且有大量的应用：在一种公式中非常困难的计算在全息对偶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。该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，以及特定的CFTs。这样的对应关系可以具有应用，例如，在凝聚态物理学中，通过与对数CFT对偶的引力理论来描述具有淬灭无序的强耦合系统。在另一个方向应用对应可能会导致新的见解四维量子引力在AdS通过研究其对偶CFT。

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.