Final Report Summary - GRAVQUANTMAT (Gravity, Black Holes and Strongly Coupled Quantum Matter) Understanding the properties of strongly coupled quantum matter poses huge conceptual challenges because standard perturbative techniques break down at strong coupling. Such states appear in awide variety of settings in condensed matter and also in the quark-gluon plasma created in the high-energy collisions of nuclei. The project has made significant theoretical progress in understanding strongly coupled matter using the remarkable tool of gauge-gravity duality, also known as the AdS/CFT correspondence. Indeed, specific strongly coupled field theories have been studied using a dual, weakly coupled gravitational description. Furthermore, this duality states that the phase structure of the quantum field theory at finite temperature is precisely described by black hole geometries and so the work has also uncovered many new aspects of black hole physics.The work has extended our understanding of known strongly coupled quantum critical ground states using novel gravitational solutions. In particular, new insights into Drude metals have been found and novel metals and insulating states have also been discovered. The phase structure of strongly coupled quantum field theories at finite temperature has been studied and new insights into spatially modulated phases have been found that exhbit striking lattice structures. A remarkable result, and a major achievement of the project, is the discovery that the thermoelectric DC conductivity matrix in gauge-gravity duality can be obtained, universally, by solvingNavier-Stokes equations on black hole horizons. It is a surprising fact that this observable, governing near equilibrium physics, is captured by the black hole horizon geometry in an analogous way to the famous result of Bekenstein and Hawking that the entropy is captured by the area of the black hole horizon. Our result can be viewed as a precise manifestation of the "membrane paradigm" in black hole physics and has also been very useful in practical calculations.The behaviour of strongly coupled systems in situations out of thermal equilibrium has also been studied. General results on diffusive processes for inhomogeneous media were obtained using gravitational tools. A new set of tools to study quantum critical ground states of string theory were developed and this led to some important results that should also lead to additional research both within the string theory and the pure mathematics communities.
