Notes on Superconformal Representations in Two Dimensions

TL;DR

This paper analyzes superconformal representations in two dimensions, decomposing multiplets, deriving character formulas, and identifying conserved charges related to super Virasoro algebra with extended supersymmetry.

Contribution

It provides a detailed decomposition of superconformal multiplets and introduces conserved charges as k-forms, advancing understanding of 2D superconformal theories.

Findings

Decomposition of superconformal multiplets using Racah-Speiser algorithm

Derivation of character formulas for superconformal representations

Identification of conserved charges as k-forms in super Virasoro algebra

Abstract

We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using Racah-Speiser algorithm, revealing many essential aspects of superconformal theories such as stress-energy tensor, conserved current, supersymmetric deformation and supersymmetry enhancement. Character formulae for the representations are presented. We further find a collection of conserved charges that are $k$-forms under the R-symmetry, which must be part of the super Virasoro algebra with $\mathcal{N} \geq 3$ supersymmetries.