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Gauge/gravity duality and its applications to condensed matter physics

Final Report Summary - GGRAVDCMPSOTON (Gauge/gravity duality and its applications to condensed matter physics)

This proposal aims to develop techniques of gauge/gravity duality for understanding thermodynamic and hydrodynamic properties of various condensed matter systems (e.g. quantum matter with exotic symmetries and superconductors), which may lead to application in areas such as quantum phase transitions and high Tc superconductivity. The novel modelling employed here may allow to characterise some of the most complex, and less understood areas of strongly coupled systems (e.universal corner contributions to entanglement negativity in conductivity) in terms of calculable observables (conductivity and entanglement entropy, etc). Moreover, in recent years it has been revealed that entanglement and holography are inherently connected, which has shed new light on understanding strongly coupled condensed matter systems in the context of holography.

In this project, we investigated several aspects along the above mentioned direction: we studied corner contributions to holographic entanglement entropy in non-conformal backgrounds: a kink for D2-branes as well as a cone and two different types of crease for D4-branes. The logarithmic term for a cone in D4-brane background was identified as the universal contribution under appropriate limits. We also studied the holographic entanglement entropy of the N = 2* theory along the whole RG flow: in the UV, the holographic entanglement entropy for arbitrary entangling region receives a universal logarithmic correction; in the IR regime the large R behaviour of the renormalized entanglement entropy suggests the emergent five-dimensional CFT in the IR. Finally we studied universal corner contributions to entanglement negativity in three- and four-dimensional CFTs using both field theory and holographic techniques. We focused on the quantity chi defined by the ratio of the universal part of the entanglement negativity over that of the entanglement entropy, which may characterise the amount of distillable entanglement. For most of the examples chi takes bigger values for singular entangling regions, which may suggest increase in distillable entanglement. However, there also exist counterexamples where distillable entanglement decreases for singular surfaces. We also explored the behaviour of chi as the coupling varies and observe that for singular entangling surfaces, the amount of distillable entanglement is mostly largest for free theories, while counterexample exists for free Dirac fermion in three dimensions. For holographic CFTs described by higher derivative gravity, chi may increase or decrease, depending on the sign of the relevant parameters. Their results may reveal a more profound connection between geometry and distillable entanglement.

The results we obtained may be contributions to a deeper understanding of the connections among quantum gravity, strongly coupled condensed matter physics and entanglement.