Symplectic Fermions

TL;DR

This paper explores the symplectic fermion conformal field theory with central charge -2, constructing its supersymmetric extension, analyzing twisted states and orbifold models, and connecting to logarithmic CFTs and critical dense polymers.

Contribution

It provides a detailed construction of the symplectic fermion CFT, including twisted states, orbifold models, and explicit correlation functions, linking to known logarithmic CFTs and polymers.

Findings

Constructed the maximal local supersymmetric conformal field theory from symplectic fermions.

Derived modular invariant partition functions for orbifold models.

Explicitly computed correlation functions for cyclic orbifolds.

Abstract

We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This theory has central charge c=-2 and provides the simplest example of a theory with logarithmic operators. Twisted states with respect to the global SL(2,C)-symmetry of the symplectic fermions are introduced and we describe in detail how one obtains a consistent set of twisted amplitudes. We study orbifold models with respect to finite subgroups of SL(2,C) and obtain their modular invariant partition functions. In the case of the cyclic orbifolds explicit expressions are given for all two-, three- and four-point functions of the fundamental fields. The C_2-orbifold is shown to be isomorphic to the bosonic local logarithmic conformal field theory of the triplet algebra encountered previously. We discuss the relation of the C_4-orbifold to critical dense polymers.