Generalized AdS4/CFT3 dualities

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.

A highlight of this project was our generalization of an AdS4 /CFT3 duality in conformal gravity by discovering a novel set of consistent boundary conditions that allow for a condensate of partially massless gravitons. In the following I explain what all these technical terms mean and why this result is significant.The holographic principle was put forward by t Hooft and Susskind in the early 1990ies. It states that one can describe the same physical situation using two apparently different theories in different dimensions. The higher-dimensional theory is a quantum theory of gravity and the lower- dimensional one a quantum theory without gravity. Holography found its most concrete realization so far in Maldacenas Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence (also known as duality). AdS stands for a relatively simple spacetime that curves like a saddle, and CFT denotes a specific type of quantum field theory where scales do not matter.The main purpose of our joint project between TU Wien and LMU Munich was to generalize AdS/CFT, particularly in the case where the gravity theory lives in four and the field theory in three spacetime dimensions hence the project name Generalized AdS4/CFT3 dualities.In the example mentioned in the opening paragraph we considered a specific scale invariant theory of gravity, known as conformal gravity, and studied which sets of boundary conditions allow for a consistent holographic description. We discovered a novel set of boundary conditions that is more general than the usual ones and were able to interpret the additional terms allowed by our set as a condensate of partially massless gravitons.Partially massless gravitons are a generalization of the usual massless gravitons known from Einsteins general relativity; more general gravity theories can have massless and massive gravitons. Conformal gravity is special due to scale invariance and does not allow massive gravitons; the additional gravitons existing in this theory are called partially massless as they have 4 degrees of freedom, which is more than massless gravitons (2) but less than massive gravitons (5).We have pursued this line of research in 25 scientific publications between 2012 and 2015 in collaboration with several postdocs and PhD students, see the final project report for details. Besides the generalization within conformal gravity we studied also generalizations to higher spin theories and the so-called AdS/log CFT correspondence. The evidence we have accumulated points to the conclusion that AdS/CFT works in far greater generality, in particular in non-standard theories of gravity and higher spin theories.