Abstract
The field space entanglement entropy of a quantum field theory is obtained by integrating out a subset of its fields. We study an interacting quantum field theory consisting of massless scalar fields on a closed compact manifold M. To this model we associate its Lifshitz dual model. The ground states of both models are invariant under constant shifts. We interpret this invariance as gauge symmetry and subject the models to proper gauge fixing. By applying the heat kernel regularization one can show that the field space entanglement entropies of the massless scalar field model and of its Lifshitz dual are agreeing.
Highlights
In quantum physics the entanglement entropy is a powerful and intriguing observable and has become the subject of intensive investigation during the last decade
Correlation functions of a n dimensional interacting quantum field theory are coinciding with the large equal-time correlation functions of an associated “dual” Lifshitz model in (n + 1) dimensions
As outlined in the previous section we interpret the Lifshitz model as being associated to the Fokker–Planck Hamiltonian arising in the stochastic quantization of the gauge model of massless scalar fields (1)
Summary
In quantum physics the entanglement entropy is a powerful and intriguing observable (for reviews see [1,2]) and has become the subject of intensive investigation during the last decade. Correlation functions of a n dimensional interacting quantum field theory are coinciding with the large equal-time correlation functions of an associated “dual” Lifshitz model in (n + 1) dimensions. Kelnhofer / Physics Letters B 775 (2017) 229–232 to which extent the field space entanglement entropies of quantum field theories and their Lifshitz duals are agreeing. As a consequence the issue of comparing field space entanglement entropies of quantum field theories and of their Lifshitz duals can be addressed.
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