Analysis of the Entanglement with Centers

TL;DR

This paper investigates entanglement entropy and mutual information in various quantum field theories, analyzing the role of centers and proving properties like strong subadditivity, with results applicable to higher-dimensional and conformal theories.

Contribution

It introduces a method to analyze centers in quantization algebras, calculates entanglement entropy in p-form theories, and demonstrates mutual information independence from centers.

Findings

Universal entanglement entropy terms relate to zero-form theories.

Strong subadditivity holds in non-interacting theories with centers.

Mutual information in 2D CFT is independent of center choices.

Abstract

We begin from the quantization algebras and constraint for analyzing the choice of centers in the first-order formulation without losing generality. Then we calculate the entanglement entropy in the non-interacting $p$-form theory in $2p+2$ dimensional Euclidean flat background with an $S^{2p}$ entangling surface. The universal term of the entanglement entropy in the non-interacting $p$-form theory is determined in terms of the universal terms of the non-interacting zero-form theory. We also prove the strong subadditivity in the non-interacting theory with the non-trivial centers. Finally, we calculate the mutual information with centers in two-dimensional conformal field theory. The result shows that the mutual information is independent of the choice of centers.