@Bergshoeff:2016soe] and in [@Bergshoeff:2017btm], theories of Carrollian (i.e., ultra-relativistic) gravity have been developed and analyzed. In particular, in [@Bergshoeff:2016soe] the authors focused on the construction of non- and ultra-relativistic Chern-Simons (CS) type actions in $2+1$ dimensions including a spin-3 field coupled to gravity. In [@Bergshoeff:2015wma], the geometry of flat and curved (Anti-de Sitter, AdS for short) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case were investigated. Afterwards, in the work [@Matulich:2019cdo], which concerns the classification of gravitational theories in $2+1$ dimensions and limits of their actions, the AdS Carroll CS gravity theory was discussed for the first time.

It has further been shown that non-relativistic symmetry groups play a remarkable role in various holography contexts [@Bagchi:2009my; @Christensen:2013lma; @Christensen:2013rfa; @Hartong:2014oma; @Bergshoeff:2014uea; @Hartong:2015wxa; @Bagchi:2010eg; @Bagchi:2012cy; @Bagchi:2016bcd; @Lodato:2016alv; @Bagchi:2019xfx; @Duval:2014uva; @Duval:2014lpa; @Ciambelli:2018xat; @Ciambelli:2018wre; @Ciambelli:2018ojf; @Campoleoni:2018ltl]. In particular, in [@Bagchi:2010eg] connections among the Bondi-Metzner-Sachs (BMS) algebra,[^1] Carrollian physics, and holography of flat space were noticed and followed up in [@Bagchi:2012cy] (see also [@Bagchi:2016bcd; @Lodato:2016alv], the latter developed in the context of supergravity, and [@Bagchi:2019xfx]). Moreover, in [@Duval:2014uva; @Duval:2014lpa] conformal extensions of the Carroll group were explored and related 