Operator product expansion and zero mode structure in logarithmic CFT

Abstract

The generic structure of 1-, 2-and 3-point functions of fields residing in indecomposable representations of arbitrary rank are given. These in turn determine the structure of the operator product expansion in logarithmic conformal field theory. The crucial role of zero modes is discussed in some

A note on four‐point functions in logarithmic conformal field theory

“…In these notes, we generalize LCFT to the case of Jordan cells of arbitrary rank, but we will restrict ourselves to the Virasoro algebra as the chiral symmetry algebra to keep things simple. As has been shown in [7,9], the generic form of 1-, 2-and 3-pt functions can be fixed up to structure constants under mild assumption on the structure of the indecomposable representations. From this, the general structure of the OPE can then easily be obtained.…”

On the gl(1|1) Wess-Zumino-Witten model

“…Let's suppose we concentrate on a projective representation primary Ψ h 1 that is mapped to Φ h 1 by the scaling operator L 0 . 9 We thus want to study the global conformal Ward identity in the case in which we have a first insertion with a logarithmic partnerδ…”

“…The c = −2 symplectic fermions are akin to a bc ghost system with two extra conjugate zero modes [9]. These extra zero modes are crucial to realize the Jordan block structure of the logarithmic conformal field theory.…”

“…The typical representations can be replaced by any ordinary Virasoro primary for the reasoning that follows 9. The projective representation will necessarily have conformal dimension zero.…”

“…The typical representations are also projective, strictly speaking. We reserve the word projective for the four-dimensional representations, for ease of expression.2 See e.g [9]. for a detailed discussion of fermionic zero modes in the bc ghost system, in contrast to the symplectic fermion model.…”