mgr Tomasz Trześniewski

The deformed Carroll particle from 3d gravity

Classical gravity in 2+1 dimensions can be formulated as the Chern-Simons theory with a local isometry group as the gauge group. Point particles may be coupled to this theory in a natural way. In principle one can then integrate out the gravitational degrees of freedom and obtain the effective particle action but in the case of de Sitter space it is rather difficult. On the other hand, de Sitter gauge group locally factorizes into the Lorentz group and the group AN(2). For vanishing cosmological constant, corresponding to the flattening of the AN(2) component one recovers a particle in flat spacetime and with the momentum space given by the Lorentz group. It turns out that if one instead flattens the Lorentz component it leads to the ultrarelativistic particle solution, known as the Carroll particle but with the AN(2) momentum space. Interestingly, the AN(2) group is related to the three-dimensional kappa-Poincare algebra, a well-studied example of deformations of relativistic symmetries which hypothetically arise in the quantization of gravity.