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

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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.