NL zoom meetings 2020/2021

Session 4: Carroll geometry and its applications (Sept. 3)

Seminars and discussions on Carroll geometry and its applications

 

13.30 – 14.00 Charles Marteau (Ecole Polytechnique, Palaiseau)

14.00 – 14.30 Laura Donnay (Vienna)

14.30 – 14.40 break

14.40 – 15.10 Luca Romano (Groningen)

15.10 – 15.40 Watse Sybesma (Iceland University)

 

15.40 – 16.00 break

16.00 – 17.00 discussion session with speakers and participants 
moderated by Stefan Vandoren

 

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Titles and Abstracts:

 

Speaker: Charles Marteau

 

Title: A new asymptotic symmetry in 3d pure gravity.

 

Abstract: I will discuss a solution space in the context of 3-dimensional pure gravity that captures a new degree of freedom, invisible in the usual Bondi gauge. In AdS, this new d.o.f. is interpreted as a choice of Cartan frame to describe the boundary metric while in flat space it becomes a choice of Ehresmann connection for the boundary Carroll structure. This new d.o.f. gives rise to new symmetries. In AdS they are nothing but a bulk realisation of the boundary local Lorentz transformations and in flat space they correspond to their Carrollian counterpart. This is consistent with the fact that the flat limit in the bulk corresponds to an ultra-relativistic (or Carrollian) limit on the boundary. I will conclude with some comments on the charges associated to these symmetries.

 

 

Speaker: Laura Donnay

 

Title: Carrollian physics at the black-hole horizon

Abstract: In this talk, I will show that the near-horizon geometry of a black hole can be described as a Carrollian geometry emerging from an ultra-relativistic limit.  The laws governing the dynamic of a black hole horizon, the null Raychaudhuri and Damour equations, are shown to be Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor. Vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killings, include BMS-like supertranslations and superrotations, and have non-trivial associated conserved charges. If time allows, I will discuss their relation with the infinite-dimensional horizon charges of the covariant phase space formalism.

 

Speaker: Luca Romano

Title: Carroll vs Galilei from a Brane Perspective

Abstract: We define a formal map between the p-brane Carroll and Galilei algebras. Under the action of this map the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. We give some applications of this map. In particular we show that it extends to the corresponding Lie algebra expansion of the Poincaré algebra. We thus generalize to p-brane Carroll our previous results on the application of the Lie algebra expansion technique to the Einstein-Hilbert action to inspect the non-relativistic regimes. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background.

 

Speaker: Watse Sybesma

Title: Carroll symmetry and the Friedmann equations

Abstract: Carroll symmetry arises from Lorentz symmetry upon taking the limit of vanishing speed of light in a controlled manner. I will discuss properties of perfect fluids with Carroll symmetry and address subtleties of how to obtain these fluids explicitly. I will furthermore argue that fluids with Carroll symmetry can be useful in the context of cosmology when considering the Friedmann equations.