Shivang Goyal | Searcharxiv

arXiv2020

Dirac fermion, cosmological event horizons and quantum entanglement

We discuss the field quantisation of a free massive Dirac fermion in the two causally disconnected static patches of the de Sitter spacetime, by using mode functions that are normalisable on the cosmological event horizon. Using this, we compute the entanglement entropy of the vacuum state corresponding to these two regions, for a given fermionic mode. Further extensions of this result to more general static spherically symmetric and stationary axisymmetric spacetimes are discussed. For the stationary axisymmetric Kerr-de Sitter spacetime in particular, the variations of the entanglement entropy with respect to various eigenvalues and spacetime parameters are depicted numerically. We also comment on such variations when instead we consider the non-extremal black hole event horizon of the same spacetime.

hep-th↗

arXiv2019

Emergent $α$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime

We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $R\cup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, the analytic continuation does not preserve the orthogonality of the resulting global modes. Accordingly, we need to orthonormalise them following the Gram-Schmidt prescription, prior to the field quantisation in order to preserve the canonical anti-commutation relations. We observe that this prescription naturally incorporates a spacetime independent continuous parameter, $θ_{\rm RL}$, into the picture. Thus interestingly, we obtain a naturally emerging one-parameter family of $α$-like de Sitter vacua. The values of $θ_{\rm RL}$ yielding the usual thermal spectra of massless created particles are pointed out. Next, using these vacua, we investigate both entanglement and Rényi entropies of either of the regions and demonstrate their dependence on $θ_{\rm RL}$.

hep-th↗