Applied Newton-Cartan Geometry

The field of Applied Newton-Cartan Geometry is currently a rapidly developing field which is attracting researchers from different directions. Recent studies of non-AdS holography involving Lifshitz spacetimes have led to field theories with non-relativistic scaling, that are coupled to an extension of Newton-Cartan geometry that includes so-called twistless torsion. Parallel to this development, effective field theories in a Newton-Cartan background have been studied in Condensed Matter Physics and used to describe a variety of non-relativistic systems such as the Fractional Quantum Hall Effect, chiral superfluids and simple fluids. Besides the holographic and effective field theory applications, there have been many other recent applications of Newton-Cartan geometry in different fields ranging from hydrodynamics to modified gravity, and even connections to String Theory. For instance, it has been shown that Hořava-Lifshitz gravity and novel extensions can be described using dynamical Newton-Cartan geometry. Furthermore, Newton-Cartan geometry obeys a duality with its ultra-relativistic cousin, Carroll geometry. Carroll symmetries have been shown to occur as symmetries of strongly coupled gravity and, more recently, of plane gravitational waves while a conformal extension of it is related to the so-called BMS symmetry of flat-space holography. Finally, studying supersymmetric non-relativistic field theories on curved Newton–Cartan backgrounds enables one to apply powerful localization techniques to extract exact non-perturbative results for these field theories such as the partition function and the vacuum expectation value of Wilson lines.

The aim of this interdisciplinary topical workshop is to advance these recent exciting applications of NC geometry in different directions. It will enable participants from different backgrounds (Condensed Matter Physics, Mathematics, Statistical Physics, Gravity and String Theory) to interact and exchange new ideas. The first topical workshop on Applied Newton-Cartan Geometry was organised in March 2017 at the Simons Center for Geometry and Physics in Stony Brook (USA), see the webpage http://scgp.stonybrook.edu/archives/18337. This workshop was a huge success and led to many contacts across different disciplines which otherwise would never have been established. New directions where set in motion like novel applications of massive gravity in the Fractional Quantum Hall Effect, the role of hydrodynamics without boost invariance and new applications of torsion in holography and Condensed Matter Physics.The aim of this workshop is to repeat the success of the Simons workshop and to give a significant boost to the emerging field of Applied Newton-Cartan Geometry and its cross-disciplinary opportunities.