Entanglement wedge cross section for noncommutative Yang-Mills theory

TL;DR

This paper investigates how noncommutativity affects entanglement measures in holographic super Yang-Mills theory, analyzing entanglement entropy, entanglement wedge cross-section, and mutual information across different energy domains.

Contribution

It provides a systematic analytical and numerical study of entanglement entropy, entanglement wedge cross-section, and mutual information in noncommutative Yang-Mills theory, highlighting UV/IR mixing effects.

Findings

Identification of a critical length scale $l_c$ indicating UV/IR mixing.

Leading order noncommutative corrections to the entropic $c$-function.

Behavior of entanglement measures across UV, noncommutative, and IR domains.

Abstract

The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length $l$. The relationship between the subsystem size (in dimensionless form) $\frac{l}{a}$ and the turning point (in dimensionless form) introduces a critical length scale $\frac{l_c}{a}$ which leads to three domains in the theory, namely, the deep UV domain ($l< l_c$; $au_{t}\gg 1$, $au_{t}\sim au_{b}$), deep noncommutative domain ($l> l_c,~au_{b}>au_t\gg 1$) and deep IR domain ($l> l_c,~au_t\ll 1$). This in turn means that the length scale $l_c$ distinctly points out the UV/IR mixing property of the non-local theory under consideration. We have carried out the holographic study of entanglement entropy for each of these domains by employing both analytical and numerical techniques. The broken Lorentz symmetry induced by noncommutativity has motivated us to redefine the entropic $c$-function. We have obtained the noncommutative correction to the $c$-function upto leading order in the noncommutative parameter. We have also looked at the behaviour of this quantity over all the domains of the theory. We then move on to compute the minimal cross-section area of the entanglement wedge by considering two disjoint subsystems $A$ and $B$. On the basis of $E_P = E_W$ duality, this leads to the holographic computation of the entanglement of purification. The correlation between two subsystems, namely, the holographic mutual information $I(A:B)$ has also been computed. Moreover, the computations of $E_W$ and $I(A:B)$ has been done for each of the domains in the theory. We have then briefly discussed the effect of the UV cut-off on the IR behaviours of these quantities.