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

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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 L₀ is diagonal and for certain values of the deformation parameters even the whole global conformal group is non-logarithmic.