  A conformal field theory (CFT) is a quantum field theory which is invariant
under conformal transformations; a group action that preserve angles but not
necessarily lengths. There are two traditional approaches to the construction
of CFTs: analyzing a statistical system near a critical point as a euclidean
field theory, and in holographic duality within the context of string theory.
This pedagogical paper presents a construction of CFTs using purely group
theoretic techniques. Starting with the basic definition of a Lie algebra and
quantum field theory, we generalize to affine Lie algebras and form a energy
momentum tensor via the Sugawara construction.
