Lifshitz holography: hydrodynamics and the large-D limit

Projektbeschreibung

Zusammenhänge in Dualitäten erkennen

In der Physik lauern scheinbar hinter jeder Ecke spannende aber auch frustrierende Dualitäten. Die allgemeine Relativitätstheorie erklärt die Schwerkraft im herkömmlichen Sinne – das heißt, warum wir nicht von unserer sich drehenden Erde geschleudert werden, die Umlaufbahnen der Planeten und sogar die Expansion des Universums. Die Quantengravitation versucht die Schwerkraft in Situationen zu erklären, in denen Quanteneffekte nicht außer Acht gelassen werden können, zum Beispiel in der direkten Umgebung schwarzer Löcher. Bei Fragen der Quantengravitation hat die Wissenschaft mit weiteren Dualitäten wie dem Paradebeispiel der sogenannten Holographie, der „AdS/CFT-Korrespondenz“ oder der Eichtheorie-/Gravitationsdualität zu tun. Das EU-finanzierte Projekt HoloLif wird sich der Lifschitz-Holographie, einem Spezialfall dieser Dualität, annehmen, um neues Licht auf wichtige Theorien und Anwendungen der Physik und Mathematik zur Beschreibung unserer Teilchen-Welt zu werfen.

Ziel

Holography is the powerful statement that two seemingly distinct theories, a theory of gravity and a field theory, describe the same physics. In this proposal I focus on Lifshitz holography, a not very well understood version of the duality, that relates non-relativistic strongly-coupled field theories and gravity realized on Lifshitz spacetimes. The aim of the project is to further develop Lifshitz holography by taking advantage of recent progress in non-relativistic hydrodynamics and the development of the large-D tool. The research objectives(ROs), each forming a separate work package, are: - Flesh out the connections between gravity and fluid dynamics for non-relativistic theories, by developing the membrane paradigm for Lifshitz black holes. This will not only be a milestone in our understanding of Lifshitz holography itself and prepare the ground for a fully-fledged non-relativistic fluid/gravity correspondence, but it will also elucidate the infrared properties of these theories, identify universal behaviours in transport coefficients and other observables and explore the generality of recently-proposed connections between hydrodynamics, non-hydrodynamic modes and chaos. - Extend the large-D tool to Lifshitz spacetimes and then use it to study holographically thermal transport in Lifshitz theories. The large-D is a technical development in general relativity realised on Anti-deSitter and flat spacetimes that leads to major simplifications of gravitational dynamics and thus eases the complexity of calculations. This objective will impact both holographic studies and gravity considerations in Lifshitz spacetimes. To achieve these ROs, I will mainly study various aspects of quasinormal modes. These modes not only contain information about black hole dynamics in the sense of characterising the dissipation of the perturbed horizon, but they are also associated with poles of the corresponding real-time Green's functions in a holographically dual theory.