Correlation Functions in N=3 Superconformal Theory

TL;DR

This paper develops a superspace framework for N=3 superconformal theory, deriving solutions to super Ward identities and characterizing correlation functions as su(2) representations, revealing constraints on admissible fields.

Contribution

It introduces a superspace approach to N=3 superconformal symmetry, providing explicit solutions to Ward identities and a method to construct all su(2) representations of correlation functions.

Findings

Correlation functions are su(2) representations.

Admissible fields are isospin singlets and doublets.

Explicit form of N=3 n-point functions is derived.

Abstract

Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also functions of Grassmann variables (in particular correlation functions and their linear combinations) to be su(2) representations. As a consequence, the only admissible fields in the theory are isospin singlets and doublets. We show how to compute the generic form of any N=3 n-point function and demonstrate a construction of all su(2) representations on the space of N=3 superfunctions.