Periodic Reporting for period 1 - HoloLif (Lifshitz holography: hydrodynamics and the large-D limit)
Reporting period: 2019-10-01 to 2021-09-30
The gauge/gravity duality (also known as holography) states that strongly interacting systems have a weakly coupled description in terms of classical gravity in one dimension higher and thus has been a very powerful tool in investigating the dynamics of strongly coupled quantum states of matter (such as high-temperature superconductors and the Quark-Gluon plasma) that are not amenable to analysis using conventional perturbative techniques or lattice simulations. The best understood realisation of the duality involves relativistic systems that are dual to gravitational physics in spacetimes that approach the so-called Anti-de-Sitter (AdS)spacetime asymptotically. The focus of this proposal is on a much subtler and less well-understood version of the duality, namely non-relativistic holography.
Specifically, the proposed research focuses on holographic models that describe strongly coupled theories that admit Lifshitz symmetry: these are characterised by an anisotropic scaling of space and time and are thus intrinsically non-relativistic. The main aim of this action is to make progress on understanding non-relativistic holography better as well as exploring the properties of strongly coupled Lifshitz systems. This is achieved by studying gravitational quasinormal modes (QNMs). QNMs are damped oscillation modes and are particularly important in holography because they contain information about black hole dynamics in the sense of characterising the dissipation of the perturbed horizon.
In this project we have calculate the gravitational QNMs for 2 distinct models that they give rise to Lifshitz dynamics. We found significant differences between the two models in terms of dissipation. Comparing our results with the already developed Lifshitz hydrodynamics, these results may have implications regarding the viability of one of the models for real-world systems. We also made progress on the radius of convergence of hydrodynamics and the phenomenon of pole-skipping from systems with charge in AdS, which is relevant for the 2 models of interest given also carry charge and was necessary for building intuition.
To understand the origin of these differences in terms of dissipation on the gravity side of the duality, we took a step back and developed a framework for analytically extracting the hydrodynamic modes from the black hole horizon in asymptotically AdS spacetimes with the view of applying this to the Lifshitz case in the sequence.
Along the way we have also fleshed out other connections between fluids and gravity, including gravitational turbulence and superfluid lattices.
Specifically, the proposed research focuses on holographic models that describe strongly coupled theories that admit Lifshitz symmetry: these are characterised by an anisotropic scaling of space and time and are thus intrinsically non-relativistic. The main aim of this action is to make progress on understanding non-relativistic holography better as well as exploring the properties of strongly coupled Lifshitz systems. This is achieved by studying gravitational quasinormal modes (QNMs). QNMs are damped oscillation modes and are particularly important in holography because they contain information about black hole dynamics in the sense of characterising the dissipation of the perturbed horizon.
In this project we have calculate the gravitational QNMs for 2 distinct models that they give rise to Lifshitz dynamics. We found significant differences between the two models in terms of dissipation. Comparing our results with the already developed Lifshitz hydrodynamics, these results may have implications regarding the viability of one of the models for real-world systems. We also made progress on the radius of convergence of hydrodynamics and the phenomenon of pole-skipping from systems with charge in AdS, which is relevant for the 2 models of interest given also carry charge and was necessary for building intuition.
To understand the origin of these differences in terms of dissipation on the gravity side of the duality, we took a step back and developed a framework for analytically extracting the hydrodynamic modes from the black hole horizon in asymptotically AdS spacetimes with the view of applying this to the Lifshitz case in the sequence.
Along the way we have also fleshed out other connections between fluids and gravity, including gravitational turbulence and superfluid lattices.
The results of this action have been disseminated through 4 seminars/presentations, 6 scientific publications to peer-reviewed journal, participation to 5 conferences/workshops as well as a 4-week visit to IST, Lisbon. Additionally, I carrier out 3 school visits for outreach purposes and published 9 articles on my scientific outreach blog.
I have also taught a full 4th year course as an occasional lecturer and supervised a final year project. I have also been active in the scientific community, by being a referee for 2 scientific journals and co-organising an international annual meeting at Leiden University. In term of personal growth, I have secured the Royal Society-SFI University Research Fellowship, in line with my personal career development plan.
I have also taught a full 4th year course as an occasional lecturer and supervised a final year project. I have also been active in the scientific community, by being a referee for 2 scientific journals and co-organising an international annual meeting at Leiden University. In term of personal growth, I have secured the Royal Society-SFI University Research Fellowship, in line with my personal career development plan.
QNMs for Lifshitz black holes had only been studied for scalar field fluctuations. Here we computed them for gravitational fluctuations. These are more interesting than scalar ones because the corresponding fluctuations couple to conserved currents in the dual field theory. This is a computation that has been missing in the literature and connects work done in the past on Lifshitz black branes with the developments of Lifshitz hydrodynamics. It revealed big differences in terms of dissipation in the two models giving rise to Lifshitz black branes, which was not anticipated.
Being interested in the thermalisation of these systems and the radius of convergence of the associated Lifshitz hydrodynamics, we had to take a step back and first study the radius of convergence of charged relativistic systems. We found a strong dependence of the radius of convergence on the charge. In this work we also studied the phenomenon of pole-skipping, and showed that the value of the frequencies at which it occurs can be determined by analysing the behaviour of the fluctuations at the horizon. A similar behaviour is expected for Lifshitz systems given that both models carry charge. A preliminary study of pole-skipping supports this statement.
Many of the calculations involving QNMs within holography involved numerical calculation. In an attempt to understand better the behaviour of hydrodynamic modes in holography and in particular the origin of the differences in the two Lifshitz models, we developed a formalism that can extract the hydrodynamics modes analytically using properties of the horizon of the corresponding black hole. This has so far been done in the context of asymptotically Anti-de-Sitter spacetime where the duality is better understood and could now be extended to the Lifshitz case in order to understand where the difference in the 2 Lifshitz models is coming from.
In terms of further understanding the capabilities of the Large-D limit of general relativity and the connections between gravity and fluids, we have performed numerical simulations within this framework showing that gravitational theories can develop a (driven) turbulent regime, which in fact follows the celebrated Kolmogorov scaling for driven turbulence in fluids.
Last but not least, we have also studied holographic superfluids, where we have constructed Abrikosov vortical lattices. Repeating this for Lifshitz superconductor will be an interesting next step.
Being interested in the thermalisation of these systems and the radius of convergence of the associated Lifshitz hydrodynamics, we had to take a step back and first study the radius of convergence of charged relativistic systems. We found a strong dependence of the radius of convergence on the charge. In this work we also studied the phenomenon of pole-skipping, and showed that the value of the frequencies at which it occurs can be determined by analysing the behaviour of the fluctuations at the horizon. A similar behaviour is expected for Lifshitz systems given that both models carry charge. A preliminary study of pole-skipping supports this statement.
Many of the calculations involving QNMs within holography involved numerical calculation. In an attempt to understand better the behaviour of hydrodynamic modes in holography and in particular the origin of the differences in the two Lifshitz models, we developed a formalism that can extract the hydrodynamics modes analytically using properties of the horizon of the corresponding black hole. This has so far been done in the context of asymptotically Anti-de-Sitter spacetime where the duality is better understood and could now be extended to the Lifshitz case in order to understand where the difference in the 2 Lifshitz models is coming from.
In terms of further understanding the capabilities of the Large-D limit of general relativity and the connections between gravity and fluids, we have performed numerical simulations within this framework showing that gravitational theories can develop a (driven) turbulent regime, which in fact follows the celebrated Kolmogorov scaling for driven turbulence in fluids.
Last but not least, we have also studied holographic superfluids, where we have constructed Abrikosov vortical lattices. Repeating this for Lifshitz superconductor will be an interesting next step.