Holography provides a powerful tool for examining strongly coupled quantum
field theories. This technology has been adopted to try and learn about
strongly coupled systems in condensed matter physics, with a particular
focus on systems at finite charge density. I will discuss some of the
different ways this charge density can be supported in the dual
gravitational description, as well as constructing families of black hole
solutions which describe phase transitions between the different types.
Embedding such transitions within M-theory reveals a surprising way of
supporting charge through the black hole dual of a `metamagnetic' phase
transition.
