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Gravity, Black Holes and Strongly Coupled Quantum Matter

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 a
wide 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 solving
Navier-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.