On $dS_4$ extremal surfaces and entanglement entropy in some ghost CFTs

TL;DR

This paper explores the properties of ghost conformal field theories with negative central charge, examining their entanglement entropy and related features through toy models and specific ghost systems.

Contribution

It provides a detailed analysis of entanglement entropy in ghost CFTs with negative central charge, highlighting unique features like negative entropy and the role of background charge.

Findings

Negative entanglement entropy in ghost CFTs

Vacuum coincides with ghost ground state in these models

Toy models mimic key features of ghost CFTs

Abstract

In arXiv:1501.03019 [hep-th], the areas of certain complex extremal surfaces in de Sitter space were found to have resemblance with entanglement entropy in appropriate dual Euclidean non-unitary CFTs, with the area being real and negative in $dS_4$. In this paper, we study some toy models of 2-dim ghost conformal field theories with negative central charge with a view to exploring this further from the CFT point of view. In particular we consider $bc$-ghost systems with central charge $c=-2$ and study the replica formulation for entanglement entropy for a single interval, and associated issues arising in this case, notably pertaining to (i) the $SL(2)$ vacuum coinciding with the ghost ground state, and (ii) the background charge inherent in these systems which leads to particular forms for the norms of states (involving zero modes). This eventually gives rise to negative entanglement entropy. We also discuss a (logarithmic) CFT of anti-commuting scalars, with similarities in some features. Finally we discuss a simple toy model of two "ghost-spins" which mimics some of these features.