Holography and its applications
Arguably the most profound theoretical breakthough in the past 25 years has been the discovery of Holography. This by now strongly supported conjecture states a remarkable equivalence between certain strongly coupled four- dimensional quantum field theories and weakly coupled gravity theories in a negatively curved Anti-de-Sitter (AdS) spacetime with one extra dimension. Whilst this conjecture was originally formulated in a deductive (or top-down) manner in the context of string theory, it has now also been applied in an inductive (bottom-up) fashion to a wide range of physical systems including condensed matter systems, fluid mechanics, and the quark-gluon plasma thought to be created in heavy ion collisions.
Our main interest is the use of holography to study the behaviour of strongly coupled quantum systems when taken out of equilibrium and then allowed to subsequently thermalise. This process can be modeled with a tractable gravitational description in terms of an in-falling shell of energy in Anti-de-Sitter space. Using this geometrical description we have studied various probes of thermalisation, including the evolution of the energy momentum tensor, entanglement entropy of spatial regions, Wilson loops and correlation functions. We have found that in these models thermalization happens very fast (which is encouraging from the point of view of heavy ion collisions) and short-wavelength modes thermalize first.
More recently, using both numerical and analytical techniques, we have begun to apply these techniques to scenarios that more closely resemble QCD by including the effects of confinement and back-reaction to the geometric dual gravity theory. Alongside this we are developing a holographic understanding of out-of-equilibrium spectral functions in the context of condensed matter systems such as strange metals and high Tc superconductors with the aim of making contact with state of the art ultra-fast ARPES experiments.
Another recent interest related to holographic thermalisation is whether AdS is nonlinearly stable to arbitrarily small perturbations. Numerical work from 2011 suggested that spherically symmetric scalar field perturbations of arbitrarily small amplitude could lead to black hole formation in global AdS, often after many reflections from the AdS boundary, and secular growth in weakly nonlinear perturbation was identified to be responsible for the onset of energy transfer to short-wavelength modes. It was later observed, however, that other initial profiles do not lead to collapse, suggesting a complicated interplay of stable and unstable behavior. Using techniques of multiscale analysis, renormalization and averaging we have resummed the secular terms that invalidate naive perturbation theory, leading to equations describing the energy flow between modes. Results include the absense of most secular terms and the construction of three conserved charges of the flow equations.
Selected recent work in this area
Thermalization of Strongly Coupled Field Theories
By V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Muller, A. Schafer et al..
Phys.Rev.Lett. 106 (2011) 191601.