2D Conformal Field Theory and Four-point Functions of the Baby-Monster Module

Abstract

Field theoretical studies involve the evaluation of four-point Correlator functions of the involved fields. This applies equally to the calculation of Scattering Amplitudes in High Energy Physics or determining the behavior of statistical systems at critical points in Condensed matter Physics. Studying field theory for two dimensional systems with Conformal symmetry becomes important in many physical instances. In earlier studies, a dual to well known Ising model theory called Baby Monster theory has been identified. From an altogether different approach too, this theory has been developed and is of interest in mathematics of Modular forms. Inspired by this, we would like to understand the Baby Monster theory from a field theorist view point. In this work we first try to summarize some of the important concepts of Conformal Field theory in two dimensions. Main work is initiated with discussion on some of the different methods that can be used for calculating four-point functions in two dimensional conformal field theory. Eventually, using the properties and similarities arriving due to duality with Ising theory, we calculate the four-point functions of fields in the Baby-Monster theory.