Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field

TL;DR

This paper explores how deforming the Virasoro field in b,c ghost systems with arbitrary spin on branched covers leads to indecomposable representations, revealing new structures in logarithmic conformal field theories.

Contribution

It introduces a deformation approach that produces indecomposable representations in b,c ghost systems, extending understanding of LCFT structures beyond lambda=1.

Findings

For lambda=1, explicit LCFT structures are demonstrated.

Deformations lead to reducible but indecomposable representations.

A new class of indecomposable representations is identified for other lambda values.

Abstract

The Virasoro field associated to b,c ghost systems with arbitrary integer spin lambda on an n-sheeted branched covering of the Riemann sphere is deformed. This leads to reducible but indecomposable representations, if the new Virasoro field acts on the space of states, enlarged by taking the tensor product over the different sheets of the surface. For lambda=1, proven LCFT structures are made explicit through this deformation. In the other cases, the existence of Jordan cells is ruled out in favour of a novel kind of indecomposable representations.