A pseudo-conformal representation of the Virasoro algebra

TL;DR

This paper introduces a new pseudo-conformal representation of the Virasoro algebra that generalizes primary fields, encompassing ordinary and logarithmic conformal field theories, with a classification of parameters and example correlators.

Contribution

It presents a novel pseudo-conformal representation of the Virasoro algebra, extending conformal field theory frameworks with a new parametrization and classification.

Findings

Reduces to known conformal theories in special cases

Differing Green functions in certain parameter regimes

Explicit calculation of correlators for a simple example

Abstract

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary- or logarithmic-conformal field theories. This representation is parametrized by two matrices. We classify these two matrices, and calculate some of the correlators for a simple example.