Field Identifications for Interacting Bosonic Models in N=2 Superconformal Field Theory

TL;DR

This paper develops a method using free fields to analyze and classify interacting bosonic models within N=2 superconformal field theory, enabling spectrum resolution and algebra extension construction.

Contribution

It introduces a systematic approach to identify and reduce free fields in interacting models, facilitating the analysis of their spectra and algebraic structures.

Findings

Finite number of primary fields for each model's extended algebra

Method to reduce free fields to standard form

Illustrative example demonstrating the approach

Abstract

We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and their dimensions, and how we may identify different free fields as representing the same interacting field. We show how a lattice of identifying fields may be built up and how every free field may be reduced to a standard form, thus permitting the resolution of the spectrum. We explain how to build the extended algebra and show that there are a finite number of primary fields for this algebra for any of the models. We illustrate this by studying an example.