On invariants and scalar chiral correlation functions in N=1 superconformal field theories

TL;DR

This paper derives a general formula for four-point functions with zero R-charge in N=1 superconformal theories, utilizing nilpotent invariants and analyzing their dependencies to understand scalar superfield correlations.

Contribution

It introduces a universal nilpotent differential operator approach to express four-point functions and explores invariant dependencies in N=1 superconformal field theories.

Findings

Derived a general expression for four-point functions with zero R-charge.

Analyzed dependencies among nilpotent superconformal invariants.

Explored cancellations in scalar superfield four-point functions.

Abstract

A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d>1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.