Holography

A major theoretical breakthrough in the last two decades has been the discovery that gravity theories in d+1 spacetime dimensions and quantum field theories in d dimensions are intimately related via the holographic principle. This led to the AdS/CFT correspondence, stating that a theory of strings propagating in Anti de Sitter (AdS) space is equivalent to a conformal field theory (CFT) living on the AdS boundary.

Using the AdS/CFT correspondence, formidable problems at strong coupling can be mapped into easier, weakly coupled computations in the dual theory. On the one hand, this means that aspects of quantum gravity can be understood via perturbative field theory computations, and on the other hand that non-perturbative insight about quantum field theory at strong coupling can be obtained via semi-classical reasoning in string theory. This approach has numerous applications, including the theory of strong interactions, quantum cosmology and condensed matter phenomena.

We are interested in diverse facets of holography, with an emphasis on the beautiful geometric structures that emerge when supersymmetry is preserved. We have found new supergravity solutions with a dual field theory interpretation, such as AdS vacua, black holes, smooth solitons and domain walls. Some of these solutions have been obtained after constructing new consistent truncations of string theory using the techniques of G-structures and generalized geometry.

In recent years, advanced techniques in quantum field theory such as supersymmetric localization allowed to obtain new exact results with deep implications for holography. In particular, this has led to significant progress towards understanding the microscopic origin of the black hole entropy, which represents one of the main questions in quantum gravity. We have reproduced for the first time the Bekenstein-Hawking entropy of certain emblematic classes of supersymmetric AdS black holes from a microscopic field theory computation. This required clarifying the role of complexified saddles of the quantum gravity path integral in this context. Currently we are investigating the different phases of holographic CFT’s at large N and we are pushing the match between the macroscopic black hole entropy and the microscopic entropy beyond the semi-classical approximation, aiming in this way at obtaining new exact results in quantum gravity.