Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories

TL;DR

This paper explores extending ghost systems to logarithmic conformal field theories at c=-26, revealing unique behaviors and consistency conditions on Riemann surfaces, differing from the well-studied c=-2 case.

Contribution

It introduces a novel approach to logarithmic extensions of ghost systems at c=-26, highlighting differences from c=-2 and analyzing their properties on Riemann surfaces.

Findings

Virasoro mode L_0 remains diagonal in the extended theory

Logarithmic behavior depends on deformation parameters

The theory is consistent only on nontrivial Riemann surfaces

Abstract

We study the possibility of extending ghost systems with higher spin to a logarithmic conformal field theory. In particular we are interested in c=-26 which turns out to behave very differently to the already known c=-2 case. The energy momentum tensor cannot be built anymore by a combination of derivatives of generalized symplectic fermion fields. Moreover, the logarithmically extended theory is only consistent when considered on nontrivial Riemann surfaces. This results in a LCFT with some unexpected properties. For instance the Virasoro mode L_0 is diagonal and for certain values of the deformation parameters even the whole global conformal group is non-logarithmic.