Two-dimensional fractional supersymmetric conformal- and logarithmic conformal- field theories and the two point functions

TL;DR

This paper explores two-dimensional fractional supersymmetric conformal field theories, analyzing their symmetry structures and calculating two-point functions, including extensions to logarithmic superconformal theories.

Contribution

It introduces a framework for fractional supersymmetric conformal field theories and derives explicit two-point functions for supermultiplet components and their logarithmic extensions.

Findings

Derived two-point functions for supermultiplet components.

Extended analysis to logarithmic superconformal theories.

Identified symmetry structures governing the theories.

Abstract

A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by $(L_{-1},L_{0},G_{-1/(F+1)})$ and $(\bar{L}_{-1},\bar{L}_{0},\bar{G}_{-1/(F+1)})$, the two point functions of the component-fields of supermultiplets are calculated. Then the logarithmic superconformal field theories are investigated and the chiral and full two-point functions are obtained.