Applied holography (Q2800223)

The paper is devoted to the application of gauge/gravity duality to the viscosity of a strongly coupled field and charge transport in the holographic superconductor. First, a direct approach to the gauge/gravity duality is discussed noting that some ordinary quantum field theories (QFTs) are secretly theories of quantum gravity. This consideration is based on the Weinberg-Witten theorem on a QFT with a local Poincaré covariant conserved stress tensor. Gauge/gravity duality evades the Weinberg-Witten theorem. While it does not seem to be possible to define a conserved, general covariant stress tensor in gravity, it is certainly possible to define a local Poincaré constraint conserved stress tensor on the boundary of a space-time. The difference in the number of spatial dimensions gives rise to holography. A theory of gravity should have a number of degrees of freedom that grows more slowly than the volume of space. It is discussed how to interpret extra dimensions of the gravity theory from the viewpoint of the QFT. This interpretation is based on a conformal field theory (CFT) by introducing the metric describing the so-called Poincaré patch of the anti-de Sitter space and the vacuum state of a CFT. Then, the author considers the canonical example of maximally supersymmetric \(SU(N)\) Yang-Mills theory (SYM) in \(3+1\) dimensions. The viscosity of SYM is treated in the large \(N\) limit using gauge/gravity duality. First, it is found precisely what is meant by viscosity for SYM, using hydrodynamics describing energy and momentum flow. In holography, the viscosity by varying the CFT metric is extracted considering this purely from the CFT and gravity sides. By using the given stress tensor, the boundary metric is varied and the term in representation of the stress tensor that is proportional to the viscosity is isolated. By this, gravity specifies the value of viscosity. By considering the holographic superconductor, the author treats a typical phase diagram for a high-temperature cuprate superconductor and focuses on the DC resistivity as a function of temperature. The author discusses a possibility to build in the physics of a superconducting phase transition to a field theory dual to the Einstein gravity. With this aim, additionally to the stress tensor, two QFT operators are discussed, a charge current (at discussion of conductivities) and an order parameter (at discussion of phase transitions). The consideration is based on the charged black hole background and the probe limit, in which the gauge field and scalar do not back react appreciably on the metric. As a result, it is shown that a strongly interacting CFT with a charged current and scalar operator are undergoing a superfluid phase transition at nonzero charge density in a way that produces a lot of very familiar looking physics but that started from an exotic dual gravity.NEWLINENEWLINEFor the entire collection see [Zbl 1330.81019].