Browsing by Author "Takko, Heli"

Quantum entanglement is one of the biggest mysteries in physics. In gauge field theories, the amount of entanglement can be measured with certain quantities. For an entangled system, there are correlations with these measured quantities in both time and spatial coordinates that do not fit into the understanding we currently hold about the locality of the measures and correlations. Difficulties in obtaining probes for entanglement in gauge theories arise from the problem of nonlocality. It can be stated as the problem of decomposing the space of the physical states into different regions. In this thesis, we focus on a particular supersymmetric Yang-Mills theory that is holographically dual to a classical gravity theory in an asymptotically anti de Sitter spacetime. We introduce the most important holographic probes of entanglement and discuss the inequalities obtained from the dual formulation of the entanglement entropy. We introduce the subregion duality as an interesting conjecture of holography that remains under research. The understanding of the subregion duality is not necessarily solid in arbitrary geometries, as new results that suggest either a violation of the subregion duality or act against our common knowledge of the holography by reconstructing the bulk metric beyond the entanglement wedge. This thesis will investigate this aspect of subregion duality by evaluating the bulk probes such as Wilson loop for two different geometries (deconfining and confining). We aim to find whether or not these probes remain inside of the entanglement wedge. We find that, for both geometries in four dimensions, the subregion duality is not violated. In other words, the reduced CFT state does not encode information about the bulk beyond the entanglement wedge. However, we can not assume this is the case with arbitrary geometries and therefore, this topic will remain under our interest for future research.