String theory and Holography

String theory and holography 

(E.Kiritsis, F.Nitti)

String theory is a candidate for a consistent description of all known forces at the quantum level, including gravity.  The Gauge/Gravity duality, or Holographic correspondence, is one of the deepest insights that have arisen from string theory in the past 20 years. It is a conjecture that states the equivalence between a quantum field theory on one side, and a gravitational theory (or string theory) in a higher-dimensional, curved space-time on the other side.  It provides a new link between quantum field theory and geometry and for it lies at the interface between quantum field theory, string theory and general relativity. At the same time, the holographic duality provides a valuable calculational tool: when the field theory side of the correspondence is strongly coupled and has a large number of degrees of freedom, the gravity side becomes classical and can be described with standard General Relativity.

There is a large amount of on-going research focused on applying the correspondence to strongly coupled field theories such as QCD. Other applications have been suggested in the context of strongly interacting condensed-matter systems such as high-temperature superconductors and strongly correlated quantum Fermi systems. The gauge/gravity duality has also revealed an intriguing relation between the gravitational Einstein equations and the non-linear equations of fluid dynamics. In this context, dissipation in hydrodynamic systems have been related to the physics and geometry of black hole horizons. Interesting connections between holography and information theory have also emerged, with a prominent role played by entanglement in understanding how gravitational physics and classical spacetime can emerge from fundamental degrees of freedom. Holography has also been playing an important role in constructing theories of gravity which go beyond Einstein General Relativity.

In this context, the APC group is active in several directions

Holographic description of QCD and strongly coupled phases of matter

The original version of the correspondence relates string theory on a particular ten-dimensional space-time (namely the product of five-dimensional Anti-de Sitter space and a five-dimensional sphere) to a relative of QCD, i.e. the maximally super-symmetric Yang-Mills theory in four dimensions. To get closer to real-world QCD, one may adopt a phenomenological approach: using the holographic dictionary to engineer simple theories, which match the properties found in QCD (confinement, mass gap, and running of the coupling constant). This approach has allowed constructing holographic theories that provide a quantitative match of many  observables in QCD-like theories with a large number of flavors and the understanding of their phase diagram at finite temperature and baryon-number density.  These models can be  used to describe baryonic phases of matter at high density, in and out of equilibrium. This has possible interesting applications to the description of neutron stars, both in  equilibrium and  in connection with gravitational waves signals emitted by neutron star mergers. 
 

Emergent gravity and the Self-tuning of the cosmological constant

The gauge/gracvity correspondence has revived and justified old ideas in which gravity is an effective low-energy theory of a different high-energy ordinary QFT, and the graviton is a composite of the high-energy degrees of freedom.

One of the benefits of this connection is that it allows to attack from a different angle the cosmological constant problem. This  is the (theoretical)  clash between the observed small value of the cosmological constant today (bounded by the observed large scale acceleration) and the very large value of the vacuum energy one would expect from  effective field theory arguments. Researchers in the APC theory group have  proposed a framework, based on holography, that may solve this contradiction. Following this framework, our observed 4D universe is a dynamical defect (brane) embedded in a five-dimensional curved spacetime (bulk).  The fields of the Standard Model we observe are confined on the brane, while gravity can propagate in the bulk. The value of the QFT vacuum energy is de-correlated from the geometry of the four-dimensional space-time we observe. When  the model is constructed consistently with the ideas of gauge/gravity duality, the dynamics  leads, generically, to stabilization of the brane having flat spacetime geometryregardless of the localized brane vacuum energy.
 

Holographic Renormalization Group of QFTs on curved manifolds

In gauge/gravity duality, the QFT renormalization group (which describes how couplings evolve with scale) is given a geometric representation as evolution along a radial dimension of the higher-dimensional dual spacetime. In the past four years the nature of holographic RG flows,  i.e. solutions of the bulk gravitational theory which are dual to field theory RG flows  was systematically investigated by our team.

Members of the APC theory group are conducting a systematic exploration of holographic RG flows of QFT which themselves are defined on a curved spacetime. This gave rise to a very general framework for analysing holographic field theories on curved spacetimes. Some of these developments are: