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 < lc; aut » 1, aut ∼ aub), deep noncommutative domain (l > lc, aub> aut » 1) and deep IR domain (l > lc, aut « 1). This in turn means that the length scale lc 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 dis- joint subsystems A and B. On the basis of EP = EW 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 EW 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. Finally, we consider a black hole geometry with a noncommutative parameter and study the influence of both noncommutativity and finite temperature on the various measures of quantum entanglement.
Highlights
L a and the turning point introduces a critical length scale lc a which leads to three domains in the theory, namely, the deep UV domain (l < lc; aut 1, aut ∼ aub), deep noncommutative domain (l > lc, aub > aut 1) and deep IR domain (l > lc, aut 1)
We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length l
We study the effect of UV/IR mixing on the entanglement wedge-cross section (EWCS) and holographic mutual information (HMI)
Summary
In [39], it was shown that the non-zero NS-NS B-field leads to noncommutative space on the D-brane which decouples from the closed string excitations. We first compute the integral given in eq (3.7), in order to probe the relation between the subsystem size l and turning point ut It is well-known that the UV/IR mixing property is one of the most interesting aspects of this noncommutative gauge theory. From the above relations it can be observed that the deep IR limit leads to the result corresponding to the usual commutative N = 4 super Yang-Mills gauge theory (AdS5 ×S5) in 3 + 1-dimensions. As we shall see in the subsequent discussion that the deep UV solution (for l < lc) poses problems in the determination of the c-function For this we proceed to write down the expression of a2SEE|finite (given in eq (3.18) for aut in terms dimensionless form Using the above expression we can holographically compute the c-function of the dual field theory which we shall carry out
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