A study of Bosonic and Fermionic Theories at Large Charge

The aim of this thesis is to systematically and consistently study strongly coupled bosonic and fermionic conformal field theories using the large quantum number expansion. The idea behind it is to study sectors of conformal field theories that are characterised by large quantum numbers under global symmetries. In this limit, the conformal field theories, even if they initially were strongly coupled and interacting, can now be written in terms of an effective field theory that is weakly coupled. Some common effective field theories that appear in the literature are the bosonic conformal superfluid and the Fermi sphere, condensed matter systems characterised by a high particle density, making the study of such systems a cross-disciplinary matter.