Gauge Theories,
Strings and Supergravity

The difficulties that arise in formulating a theory of gravity according to the principles of quantum mechanics are longstanding, and manifest themselves most vividly in the conundrums related with the quantum properties of black holes. A naive description of the process of black hole evaporation via Hawking radiation seems to violate unitarity, a fundamental principle of quantum mechanics. The root of this difficulty lies in our lack of understanding of the nature of black hole microstates: the Bekenstein-Hawking entropy predicts an enormous number of states with fixed global charges, but these states are invisible in the spacetime picture of black holes implied by general relativity.

Holography relates the microstates of black holes to states of a dual Conformal Field Theory (CFT) and provides an invaluable tool to elucidate their properties and to formulate a consistent unitary description of their dynamics. Conversely, the identification of the microstates with explicit supergravity solutions can be used to extract non-trivial informations on the CFT. For instance, the study of small perturbations around the geometry of microstates leads to a novel way to compute dynamical correlators at strong coupling.

The main current focus of String phenomenology is the investigation of the general features that characterise effective field theories of consistent quantum gravity models. This means understanding the structure of low-energy supergravity models, their relations to string compactifications and their implications for the so-called swampland program.

The vacuum selection process is a longstanding problem of String Theory, whose solution is central for any attempt to extracting meaningful phenomenology. Most of the features of the effective 4-dimensional models one can generate from String Theory depend on the properties of the vacuum: the value of the cosmological constant, the effective particle content, their masses, couplings and most of their symmetries. Understanding the structure of low-energy supergravity models can be done by analyzing the allowed couplings, vacua and especially their supersymmetry breaking patterns. Time and again we have been explicitly constructing models in various dimensions that had not been previously analyzed, fully or in part. We have developed new techniques to find, study and classify vacua in gauged supergravities and we are currently understanding their relation to higher-dimensional theories.

Low energy supergravity models are plagued by a huge number of moduli (massless scalar fields), whose expectation values determine many couplings between the fields and the resulting physics. Flux compactifications provide a simple perturbative framework in which one can address this problem. We study how this affects the geometry of the allowed internal manifolds in compactifications to 4 dimensions and spell the dictionary between 4-dimensional couplings and higher dimensional properties. We are especially interested in cases where the reduction process uses locally geometric backgrounds, where duality symmetries play a prominent role and new mathematical tools are needed.

An interesting area where such studies can be usefully applied is string cosmology. Inflation could have happened at a very high energy scale. We are therefore interested in all sorts of imprints that could be related to low-energy effects deriving from string theory.

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.