2013/12/21 by Benjamin Horowitz, Horowitz, Benjamin
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1312.6196
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.