Holographic Entanglement in a Noncommutative Gauge Theory

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.Comment: 28 pages, multiple figures; minor changes, conclusions unchange

Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential

We investigate the behavior of entanglement entropy at finite temperature and chemical potential for strongly coupled large-N gauge theories in $d$-dimensions ($d\ge 3$) that are dual to Anti-de Sitter-Reissner-Nordstrom geometries in $(d+1)-$dimensions, in the context of gauge-gravity duality. We develop systematic expansions based on the Ryu-Takayanagi prescription that enable us to derive analytic expressions for entanglement entropy and mutual information in different regimes of interest. Consequently, we identify the specific regions of the bulk geometry that contribute most significantly to the entanglement entropy of the boundary theory at different limits. We define a scale, dubbed as the effective temperature, which determines the behavior of entanglement in different regimes. At high effective temperature, entanglement entropy is dominated by the thermodynamic entropy, however, mutual information subtracts out this contribution and measures the actual quantum entanglement. Finally, we study the entanglement/disentanglement transition of mutual information in the presence of chemical potential which shows that the quantum entanglement between two sub-regions decreases with the increase of chemical potential.Comment: 38 pages, multiple figure