Ghost-spin chains, entanglement and $bc$-ghost CFTs

Abstract

We study 1-dimensional chains of ghost-spins with nearest neighbour interactions amongst them, developing further the study of ghost-spins in previous work, defined as 2-state spin variables with indefinite norm. First we study finite ghost-spin chains with Ising-like nearest neighbour interactions: this helps organize and clarify the study of entanglement earlier and we develop this further. Then we study a family of infinite ghost-spin chains with a different Hamiltonian containing nearest neighbour hopping-type interactions. By defining fermionic ghost-spin variables through a Jordan-Wigner transformation, we argue that these ghost-spin chains lead in the continuum limit to the $bc$-ghost CFTs.

Latex, 33pgs

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• de Sitter entropy as entanglement
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• N-level ghost-spins and entanglement
• Holographic timelike entanglement in AdS${}_3$ Vaidya