Chiral Green's Functions in Superconformal Field Theory

TL;DR

This paper derives unique forms of three-point chiral Green's functions in superconformal field theories with various supersymmetries by solving Ward identities, and discusses constraints on higher-point functions.

Contribution

It provides explicit solutions for three-point functions in superconformal theories and analyzes the conditions under which higher-point functions are uniquely determined.

Findings

Unique three-point Green's functions for N=1,2,3,4 supersymmetry.

Four-point function with R-charge one is determined up to four constants.

Higher-point functions with R-charge > N are not uniquely fixed.

Abstract

By solving the Ward identities in a superconformal field theory we find the unique three-point Green's functions composed of chiral superfields for N = 1,2,3,4 supersymmetry. We show that the N=1 four-point function with R-charge equal to one is uniquely determined by the Ward identities up to the specification of four constants. We discuss why chiral Green's functions above three-points, with total R-charge greater than N, are not uniquely determined.