New corner in 3D gravity: non-Lorentzian sectors and their applications to condensed matter models

Gravity is the fundamental force that is an integral part of our daily lives. Despite its ubiquity, one of the most open questions in theoretical physics is whether gravity is a geometrical phenomenon, as Einstein proposed, or governed by the law of quantum mechanics. This question leads to the formulation of a still-unknown framework called quantum gravity. A predominant model to address this problem is 3D gravity, which contains the same conceptual features as 4D Einstein theory. For decades, it has been a concrete model of quantising gravity with applications to black hole mechanics, spacetime solutions and their relation to condensed matter models, and the most fertile scenario to apply the AdS/CFT correspondence. This project focuses on formulating an intriguing new corner of 3D gravity. The latest sector is called non-Lorentzian 3D gravity, and time and the other spatial dimensions are dealt with differently as relativistic theories. I will study the foundations and dynamics of this self-contained sector with applications to the quantum Hall effect. My knowledge of non-Lorentzian topics has been gained during my PhD at CECs (Chile) and Niels Bohr Insitute (Denmark) and my postdoctoral position at the University of Iceland (Iceland), where I collaborated with world experts in non-Lorentzian aspects of physical systems. Therefore, this background on non-Lorentzian limits of physical systems makes me excellently suited for exploring other new sectors in gravity, and MCSA-PF provides me with the support to make it. The skills of this cutting-edge research will be transferred to the host organisation, Nordita and Stockholm University, via my long-term collaborations with leading institutions in the EU and Latin America. The varied research spectrum within its faculty members and postdocs makes Nordita an excellent environment for this project. The host, the EU, and I will benefit from the collaboration between the scientific networks this project will bring.