Abstract
In this paper, we derive the universal (cut-off-independent) part of the holographic entanglement entropy in the noncommutative Yang-Mills theory and examine its properties in detail. The behavior of the holographic entanglement entropy as a function of a scale of the system changes drastically between large noncommutativity and small noncommutativity. The strong subadditivity inequality for the entanglement entropies in the noncommutative Yang-Mills theory is modified in large noncommutativity. The behavior of entropic $c$-function defined by means of the entanglement entropy also changes drastically between large noncommutativity and small noncommutativity. In addition, there is a transition for the entanglement entropy in the noncommutative Yang-Mills theory at finite temperature.
Highlights
The noncommutative gauge theories discussed in this paper are gauge theories in which the product of any two fields is given by the Moyal-Weyl product [1,2]f⋆gðxÞ ≡ fðxÞ exp i 2 θμν∂⃖ μ ∂⃗ν gðxÞ; ð1:1Þ where θμν is the deformation parameter
We focus on quantum entanglement in noncommutative gauge theory
II, we introduce the holographic entanglement entropy conjectured by Ryu and Takayanagi and derive the universal part of the holographic entanglement entropy in the noncommutative Yang-Mills theory
Summary
The noncommutative gauge theories discussed in this paper are gauge theories in which the product of any two fields is given by the Moyal-Weyl product [1,2]. The holographic description of the noncommutative gauge theories is often useful to investigate how the noncommutativity (the deformation parameter) affects the quantum properties of the gauge theories. The holographic entanglement entropies for quantum field theories are often regularized by introducing an ultraviolet cutoff parameter. We try to derive the universal (cutoff-independent) part of the holographic entanglement entropy in the noncommutative Yang-Mills theory and discuss its properties. The properties of the holographic entanglement entropy in the noncommutative Yang-Mills theory should be discussed on the basis of universal (cutoff-independent) quantities.
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