Symplectic fermions in general domains

TL;DR

This paper reviews symplectic fermions, a logarithmic conformal field theory with central charge -2, focusing on their structure, correlation functions, and relevance to lattice models, making the topic accessible to newcomers.

Contribution

It provides an explicit construction of the symplectic fermions' field space and discusses their logarithmic structure and correlation functions within a bootstrap framework.

Findings

Explicit construction of the logarithmic Fock space

Analysis of the Virasoro algebra representation

Method for computing correlation functions

Abstract

We review the basic features of a logarithmic conformal field theory that arise in the context of the scaling limit of lattice models. The theory of interest is the symplectic fermions, whose central charge is $-2$. We provide an explicit construction of its space of fields as a logarithmic Fock space, and discuss its logarithmic structure as a representation of the Virasoro algebra. The construction of the correlation functions is presented following the ideas of the bootstrap approach. The text aims to be accessible to readers with little or no expertise in conformal field theory.