The holographic duality, “holography” in short, is a powerful theoretical tool discovered in the context of string theory 25 years ago. In its bottom-up formulation, holography is a duality between weakly coupled classical gravitational theories in d+1 dimensions and strongly coupled large N field theories in d dimensions which opens a new window towards a nonperturbative formulation of quantum gravity but also provides an effective method to describe quantum field theory at strong coupling. Nowadays holography has become an important complementary and highly interdisciplinary technique used in many research fields including condensed matter, hydrodynamics, quantum information, out-of-equilibrium physics, QCD and many more.
In the context of condensed matter, important new developments in the recent years have been related to the introduction of translational symmetry breaking in the dual field theory in all its forms. This is a fundamental ingredient to describe condensed matter phases and their transport properties and it was strongly motivated by unsolved questions in the realm of high-Tc superconductors and strange metallic behavior. Importantly, these new discoveries have brought an enormous impact into our modern understanding of viscoelasticity and effective theory description of dissipative systems with broken translations. The holographic methods have not only revealed several missing pieces in the hydrodynamic and effective field theory formulations but also brought to light novel universal relations regarding the physics of pseudo-goldstone modes which have been later confirmed and explained with more standard field theory computations.
Professor Matteo Baggioli from Shanghai Jiao Tong University and professor Blaise Gouteraux from École Polytechnique Paris have reviewed these exciting findings and discussed the main research directions and open questions for the future in a recent Colloquium which has been published in Review of Modern Physics, the most renowned review journal in physics.
Reference. M.Baggioli and B.Gouteraux, “Colloquium: Hydrodynamics and holography of charge density wave phases”, Review of Modern Physics