Oscar Dias STFC Fellowship - Aspects of gauge/gravity correspondences

Black hole (BH) thermodynamics and Hawking radiation suggest the existence of a statistical or microscopic description of BHs behind the scenes. This description necessarily requires quantum gravity. BHs have an entropy (a quantity that measures the disorder of the system) proportional not to its volume (as usual in other systems) but instead to its horizon's area. This suggests that the quantum information of the BH is distributed over a surface rather than on a volume and motivates the holographic principle according to which quantum gravity in a given volume should have a dual description in terms of a quantum field theory (QFT) on its boundary surface. The gravity/gauge theory dualities (correspondences) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the AdS box, where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs, QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider at CERN), superconductors and fluids. In these dualities BHs play an essential role. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. I will discover new BH solutions, study BH instabilities, and find what they correspond to in the dual language. One is the ultraspinning instability that makes fastly spinning BHs pinch into black rings (doughnut-like BHs). Another is the superradiant instability whereby radiation reflected by the AdS box amplifies its energy when it scatters a BH up to the point where it is so energetic that we have a BH bomb system. Yet another one is the gravitational turbulent instability that might teach us about one of the most mysterious processes in fluids and aerodynamics: turbulence. Unconventional high-temperature superconductors have been discovered in the lab but no theory can describe their properties satisfactorily. The gravity / condensed matter correspondence proposes that with holographic superconductors one can use gravity to model the experimental superconductors. This project will develop more realistic models of holographic superconductors to get novel insights into strongly coupled physics. Remarkably the gravity/gauge dualities can have a hydrodynamic description. The tantalising similarities between BH physics, and the properties of soap bubbles and fluid lumps, have been observed from old: A BH has a horizon with surface gravity, like a fluid droplet has a surface tension; Hawking evaporation of a BH bears a resemblance to the fluid droplet's evaporation; Black strings (tubes) pinch-off into spherical BHs much like a water jet dripping from a faucet breaks into droplets. But, albeit these analogies, only recently was a formal scientific correspondence found between gravity and hydrodynamics: hydrodynamic equations encode in a certain regime Einstein's equations! Phenomena in gravity can be studied using a dual fluid dynamic language. A goal of this project is to develop the dictionary between these scientific languages and use it to study open problems in gravity, QFT and hydrodynamics.