# $N$-level ghost spins and entanglement

Jatkar, Dileep P. (Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India) (Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India) ; Kolekar, Kedar S. (Chennai Mathematical Institute, SIPCOT IT Park, Siruseri 603103, India) ; Narayan, K. (Chennai Mathematical Institute, SIPCOT IT Park, Siruseri 603103, India)

07 May 2019

Abstract: Ghost spins, 2-level spinlike variables with indefinite norm have been studied in previous work. Here we explore various $N$-level generalizations of ghost spins. First we discuss a flavored generalization comprising $N$ copies of the ghost-spin system, as well as certain ghost-spin chains which in the continuum limit lead to 2-dim $bc$-ghost conformal field theorys with $O\left(N\right)$ flavor symmetry. Then we explore a symplectic generalization that involves antisymmetric inner products, and finally a ghost-spin system exhibiting $N$ irreducible levels. We also study entanglement properties. In all these cases, we show the existence of positive norm “correlated ghost spin” states in two copies of ghost-spin ensembles obtained by entangling identical ghost spins from each copy: these exhibit positive entanglement entropy.

Published in: Physical Review D 99 (2019)