Research
AdS/CFT Correspondence
Strongly interacting systems (SIS) are very common in Nature, famous examples ranging from the fundamental theory of quarks and gluons - Quantum Chromo-Dynamics (QCD) - to quantum critical systems, high-temperature superconductors, strange metals, quantum Hall systems and possibly even new materials as graphene. In these systems the interaction between different particles becomes so intense that the most common mathematical tools used to describe them break down and the traditional paradigms based on weakly interacting degrees of freedom cannot be applied.
A promising powerful technique to investigate SIS is the holographic correspondence, often referred to as AdS/CFT or gauge/gravity duality. It is founded on a duality map between ordinary quantum field theories (QFTs) and higher dimensional models of gravity and strings.
A typical problem one can address in this framework is the strong dynamics of hadronic matter. A first-principle approach is provided by a reformulation of QCD on Euclidean lattices and the use of numerical Monte Carlo methods. This technique, powerful when studying equilibrium properties, has still severe limitations when analyzing real-time dynamical issues or finite quark density regimes. Holography has already had some success in modelling the low viscosity fluid state of matter called Quark Gluon Plasma, which was created in heavy ion collision experiments at Brookhaven National Laboratory, and, more recently, at the LHC at CERN. Moreover in QFT models where additional symmetries are present (typically supersymmetries) exact dynamical properties of the strong coupling regime as confinement, chiral symmetry breaking and critical exponents have been derived by using gauge/gravity duality.
Boundary, Impurities, and Defects in QFT
Ryu-Takayanagi surface for the entanglement entropy in presence of a boundary
In many systems considered in physics, as in everyday life, impurities and defects are unwanted since they hide or remove desired properties and features. However, boundaries, impurities, and defects (BIDs) may, in fact, be the key to some of the most important current problems in physics —and hence to a new generation of electronics, quantum computing, energy efficiency, and more. In other words, BIDs are not a bug but a feature deserving intense study. Like Mona Lisa’s smile, at first glance, they may look like an imperfection, but after a bit of thought, they become the key to the whole picture.
Can we classify BIDs in QFT? The couplings of QFTs describe a hierarchical landscape in which Conformal Field Theories (CFTs) occupy privileged positions at extrema, and Renormalisation Group (RG) flows connect them. To date, the only claim of a complete classification of BIDs is for two-dimensional CFTs with boundaries, called Boundary CFTs. Specifically, Virasoro minimal model boundary CFTs, which, being rational CFTs, have a finite number of primary operators. What about other rational CFTs, non-rational CFTs, and higher-dimensional CFTs and QFTs more generally? To what extent can BIDs be classified by conformal symmetry alone, for example, via the conformal bootstrap or central charges? To what extent can BIDs be classified by other symmetries and their anomalies? To what extent can they be classified by their quantum entanglement structure, as measured, for example, by entanglement entropy (EE)? Clearly, the full potential of QFT tools for identifying “universality classes” of BIDs, and the implications for particle physics and condensed matter physics, is very far from being fully realized.
What theoretical constraints must BIDs obey? QFT has been helpful in condensed matter physics largely because of non-perturbative constraints that rely on minimal ingredients and hence are universal and powerful, coming from the conformal bootstrap, integrability, c-theorems, and more. However, such constraints have been explored relatively little for BIDs, especially in higher dimensions. How do the conformal bootstrap and integrability constrain correlators or the spectrum of BID systems? What c-theorems must BIDs obey, for RG flows either on the BIDs themselves or in the bulk they couple to? How do fundamental constraints such as unitarity, realized, for example, via the ANEC or strong sub-additivity of EE, constrain BIDs? Can dualities between QFTs reveal restrictions on BIDs? Clearly, universal theoretical constraints on BID systems are waiting to be discovered.
Exact Results in QFT: from Localization to integrability
Localization: the supersymmetry algebras can be sometimes deformed to accommodate background curvatures and the partition functions for the resulting quantum theories can be evaluated in a closed form via a particular saddle-point procedure, known as the supersymmetric localization. Thanks to this method, a huge number of new exact results have been derived in different contexts, for local and non-local observables: the strong coupling limits have been compared with holographic predictions, supporting in general the validity of the duality.
Integrability: This is a fundamental ingredient for understanding the gravitational/string description of certain strongly interacting gauge theories. For instance, the sigma models effectively describing their strong coupling regime are in some cases naturally endowed with an integrable structure. Quite surprisingly this property survives in the dual field theoretical picture and is used to obtain exact results at any coupling for quantities such as the spectrum of anomalous dimensions of operators in maximally supersymmetric QFTs!
Quantum Information and Black Holes
The AdS/CFT correspondence has been a driving force in developing the growing connection between quantum information theory, field theory and gravity.
The holographic prescription for computing the entanglement entropy played a central role in this respect. Allowing to evaluate the entanglement entropy of a spatial region in geometric terms in the dual AdS spacetime, it provides a direct link between classical geometry and the quantum correlation structure of dual states.
This remarkable connection is a key example of how gravity geometrizes quantum information measures and concepts. It propelled a whole new program aimed at understanding one of the most profound implications of the AdS/CFT correspondence: that a theory of quantum gravity should be fully contained in the dual CFT description, with spacetime emerging from the boundary entanglement structure.
Developments along this avenue also gave important insight into many questions in field theory and gravity, with applicability beyond the holographic framework. The proof of the irreversibility of renormalization group flows using quantum information inequalities and the discovery of new energy conditions are some key examples.
A recent striking result is the new understanding of how to evaluate entanglement entropy in semi-classical gravity, which solves important aspects of the black hole information paradox and opens a new window onto our understanding of black holes.
Holography for QCD and Dark Matter
While gravity duals of pure Yang-Mills and QCD do not exist, even in their planar limit, there exist holographic models that, in the gravity regime, share a lot of structures with these theories. The most accurate top-down holographic model of QCD (often called "Holographic QCD") is the Witten-Sakai-Sugimoto (WSS) one. It shares the same vacuum structure with QCD, it geometrizes many of its properties and it is competitive at the quantitative level with other effective theories (such as NJL, Skyrme model, etc.) in estimating the value of a variety of QCD observables. Interestingly, when applied to the finite-theta angle regime, it allows to access qualitative information about QCD which are beyond any other mean of investigation, such as the nature of the theory on QCD domain walls.
Moreover, the WSS and similar top-down holographic models can be employed to model Dark Matter (DM). The possibility that DM is due to an axion or a QCD-like hidden sector is often discussed in the literature. In such cases, some of the interesting physical phenomena (e.g. phase transitions) can happen in the strong coupling regime. Such axion models or QCD-like sectors are amenable to be modeled by the WSS and similar theories. Thus, the latter allow to study very interesting phenomena, e.g. cosmological phase transitions and the possible production of gravitational waves, whose spectra can in principle be detected by current (LIGO, VIRGO, KAGRA) and future (e.g. LISA, ET) facilities.
