Implications of N=1 Superconformal Symmetry for Chiral Fields

TL;DR

This paper analyzes the constraints of N=1 superconformal symmetry on correlation functions of chiral superfields, deriving explicit forms for three- and four-point functions and solving associated differential equations.

Contribution

It provides complete expressions for three- and four-point functions of chiral superfields under N=1 superconformal invariance, including solutions to differential equations and crossing symmetry analysis.

Findings

Derived explicit three-point functions for general spin cases.

Solved differential equations for four-point functions involving hypergeometric functions.

Established that four-point functions are determined up to a single constant by symmetry.

Abstract

The requirements of N=1 superconformal invariance for the correlation functions of chiral superfields are analysed. Complete expressions are found for the three point function for the general spin case and for the four point function for scalar superfields for \sum q_i=3 where q_i is the scale dimension for the i'th superfield and is related to the U(1) R-charge. In the latter case the relevant Ward identities reduce to eight differential equations for four functions of u,v which are invariants when the superconformal symmetry is reduced to the usual conformal group. The differential equations have a general solution given by four linearly independent expressions involving a two variable generalisation of the hypergeometric function. By considering the behaviour under permutations, or crossing symmetry, the chiral four point function is shown to be determined up to a single overall constant. The results are in accord with the supersymmetric operator product expansion.