Sommerfeld Theory Colloquium, Metals are found frequently in nature and their properties are usually

very well described within Landaus Fermi liquid theory. Various

strongly correlated materials exhibit strange metallic phases which do

not fit into the Fermi-liquid framework, however. The theoretical description

of such non-Fermi liquids remains one of the main unsolved

problems in condensed matter physics. In this talk I will give an

introduction to the problem and show how interesting strongly coupled

field theories arise in the low energy description of such states,

which are still very poorly understood. I will focus on the paradigmatic

problem of a metal coupled to fluctuations of a critical Ising

order parameter and discuss unexpected scaling properties at finite

temperature.