Carrollian physics and holography

Carrollian physics appeared for the first time out of a mathematical curiosity in a work of Lévy-Leblond: what if, instead of taking the usual non-relativistic limit of the Poincaré group where the speed of light c is taken to ∞, one considers the opposite limit, namely c→0? While the first limit gives rise to the familiar Galilean group, the second leads to the so-called Carroll group. In a Carrollian limit (c→0), the lightcones collapse along the time axis, which means that particles can no longer move and two spacetime events are causally disconnected. This absence of causality, as well as arbitrarinesses of time intervals, reminded Lévy-Leblond of Lewis Carroll's book Through the looking-glass, which is the origin for the name of this ultralocal limit of the Poincaré group.

While such spacetimes seem a priori to be too strange to be of any physical relevance, there has been recently a surge of interest in Carrollian physics. It is quite a remarkable fact that, indeed, Carrollian physics naturally appear in the context of the geometry of null surfaces and the associated Bondi-Metzner-Sachs symmetries, but also black hole horizons, inflationary cosmology, fluid/gravity and holographic correspondences, as well as limits of Einstein gravity.

The ESI programme is expected to foster further progress on the following developments:

• Carrollian fluids
• Flat space holography
• Carrollian gravity theories
• Lower-dimensional models
• Fracton physics