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Gravity duals of inhomogeneous strongly correlated fermions

Final Report Summary - GDISCF (Gravity duals of inhomogeneous strongly correlated fermions)

One of the most notable challenges for theoretical physics is to provide non-perturbative methods to describe the dynamics of strongly coupled quantum field theories. These are in fact at the basis of our current description of many relevant phenomena in Nature.

In the realm of particle physics the prototypical example is quantum chromodynamics (QCD), the fundamental theory of quarks and gluons. A first-principle approach to QCD at strong coupling is provided by a reformulation of the theory on Euclidean lattices and by the use of numerical Monte Carlo methods. This technique, powerful for what concerns the study of some equilibrium properties, has still severe limitations for what concerns the analysis of real-time dynamical issues or the study of finite quark density regimes.

Other paradigmatic examples, of high technological relevance, arise in the realm of condensed matter physics. Quantum critical systems, superconductors with a high critical temperature, ultracold Fermi gases at unitarity, quantum Hall systems, strange metals, all appear to evade most of the traditional paradigms (e.g. Landau-Fermi liquid or BCS theories) based on sharp quasiparticles or weakly coupled degrees of freedom. It is thus extremely urgent to develop novel theoretical frameworks in which these systems can be analysed.

The aim of the present research project has been to provide novel contributions - in some very specific settings, indeed - to these notable challenges. The non-perturbative tools which have been employed are based on the 'holographic correspondence' which is a map between classes of ordinary quantum field theories and higher dimensional theories of gravity. Remarkably, this allows suitably defined regimes where a quantum field theory is strongly interacting, to be described by means of a classical, weakly coupled, theory of gravity. In this way, hardly solvable quantum problems are mapped into easier, classical ones in the dual description.

The main focus of the present project has been the study of strongly correlated fermionic systems both in 3+1 dimensional QCD-like models and in 2+1 dimensional effective models for unconventional unbalanced superconductors and superfluids. Conventional superconductors with a chemical potential mismatch between spin up and down fermions are expected to develop phases with inhomogeneous and anisotropic condensates. The occurrence of these phases in stronlgly coupled setups (which also include, for example, polarised ultracold Fermi gases at unitarity and high density quark matter at the core of neutron stars) is an open issue which we would like to better understand using holographic techniques.

The present project has been developed according to the original work plan. Training has been delivered to F. Bigazzi both by discussions and lectures of the supervisor (Roberto Casalbuoni) on 'Unbalanced Fermi Mixtures in condensed matter and QCD' and by participation to working groups involving also other experts in the area (Francesco Becattini, Domenico Seminara, Francesco Matera for issues on 'Relativistic Hydrodynamics and Heavy Ion Collisions', Andrea Cappelli, Filippo Colomo, Marco Tarlini, Domenico Seminara, Francesco Bonechi, Francesco Becattini, Riccardo Giachetti, Emanuele Sorace for issues on 'c-theorem and its possible extensions'). Additional training has been provided by participation to workshops and conferences. Among them, the 2010 Workshop on AdS3/CFT4 and the quantum states of matter, and the 2011 Workshop on Large N field theories (both held at the Galileo Galilei Institute in Florence), the 2011 International School on Quark-Gluon Plasma and Heavy Ion Collisions: the past, the present, the future held in Torino and the INFN Workshop on Theories of Fundamental Interactions, Sissa, Trieste, January 2012.

Concerning the main scientific results, in collaboration with A.L. Cotrone (Torino), J. Mas (Santiago de Compostela), D. Mayerson (Amsterdam) and J. Tarrio (Utrecht), F. Bigazzi has found a family of gravity solutions in ten dimensions which provide the holographic dual description to a corresponding family of 4d non-abelian gauge theories, coupled with massless dynamical flavour fields, at finite temperature and quark density. These gauge theories arise as the low energy description of open strings attached to D3 and smeared D7 branes on Calabi-Yau spaces. The corresponding gravity solutions have allowed to compute the full thermodynamic observables at strong coupling, as well as to study dynamical issues like the quenching of jets traveling through the plasmas. Interestingly, the latter phenomenon is found to be enhanced by dynamical flavours. These results have been published in JHEP 1104 (2011) 060. Improvements of these results, including an analysis of the stability of the related gravity solutions, will be published in February 2013.

A detailed review of the above mentioned holographic quark-gluon plasmas, including also novel results on the susceptibilities and the holographic effective action have been presented in a paper written in collaboration with A.L. Cotrone, J. Mas, D. Mayerson, J.Tarrio Commun.Theor.Phys. 57 (2012) 364-386. A shorter review has been written with the same authors and A. Paredes (Barcelona) and published in PoS FACESQCD (2010) 005. Results on the hydrodynamic coefficients to second orderd have been collected in a paper written with A.L. Cotrone and J. Tarrio, Fortsch.Phys. 59 (2011) 665-670.

In collaboration with A.L.Cotrone D. Seminara, and two students (D. Musso and N.P. Fokeeva), F. Bigazzi has presented the first effective holographic models for unbalanced strongly coupled superconductors in 2+1 dimensions. The corresponding 3+1 dimensional gravity solutions carry two Maxwell fields, U(1)_A and U(1)_B, respectively dual to the 'charge' and 'spin' currents, as well as a non-trivial scalar field charged under U(1)_A, dual to an s-wave order parameter. These solutions allow to study the phase diagram of the dual models at strong coupling, where no inhomogeneous superconducting phase seems to be admitted. Moreover, they allow to study transport properties and in particular to extract the full matrix of charge, spin, heat and mixed conductivities. The latter shows the occurrence of mixing effects between charge and spin currents which are analogous to the ones at the basis of 'spintronics', the field of research which deals with spin transport. These effects appear to be a universal prediction of holographic models. Another interesting outcome is the prediction that the spin conductivity is enhanced in the superconducting phase. The model presented by F. Bigazzi and collaborators provides the first holographic realisation of spintronic effects, opening the possibility to studying their occurrence in strongly coupled setups. These results have been published in JHEP 1202 (2012) 078. Improvements of these results, with a complete scan of the parameter space of the model, are being considered and will hopefully be published in 2013.