Entanglement entropy and nonabelian gauge symmetry

By William Donnelly. 2014

176 citations recorded by the source corpus.

Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2606a94e9acec622b879d0ed85a37e460b7c76df

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Citations in the corpus

Observables, gravitational dressing, and obstructions to locality and subsystems (2016, background): “Specifically, a proposed definition of entanglement of gauge theories in terms of subalgebras of compactly supported gauge-invariant observables [28] does not agree with a Hilbert space definition of entanglement [29], due to contributions of Wilson lines that “cross the boundary” between the subsys”
Local subsystems in gauge theory and gravity (2016, background): “[22] it is shown that such states are necessary for consistency of the thermal description of the de Sitter vacuum.”
Geometric entropy and edge modes of the electromagnetic field (2015, background): “a state-counting interpretation related to edge modes, as elucidated in [23, 35, 46].”
Entanglement entropy: Holography and renormalization group (2018, background): “For discussions and attempts to define entanglement entropy in gauge theories, see e.g. (Aoki et al., 2015; Casini et al., 2014; Chen et al., 2015; Donnelly, 2014; Donnelly and Wall, 2015, 2016; Ghosh et al., 2015; Hung and Wan, 2015; Ma, 2016; Pretko and Senthil, 2016; Radicevic, 2014, 2016; Soni…”