Carrollian ABJM: Fermions and Supersymmetry

TL;DR

This paper explores the flat space limit of the ABJM theory, revealing a Carrollian superconformal structure with implications for flat space holography and M-theory dualities.

Contribution

It demonstrates how the flat space limit of ABJM theory leads to a Carrollian superconformal symmetry, including fermionic sectors, extending the understanding of flat space holography.

Findings

Identifies four realizations of Carrollian fermions from relativistic fermions.

Shows the $c ightarrow0$ limit of ABJM exhibits Carrollian superconformal symmetry.

Connects the symmetry to the extended BMS$_4$ algebra and flat space holography.

Abstract

A natural approach for constructing a concrete example of flat space holography is to take the flat space limit of a well-understood example of AdS/CFT, such as the one relating M-theory in AdS$_4$ times an orbifolded 7-sphere to a certain three dimensional superconformal Chern-Simons-matter theory known as the ABJM theory living in the boundary of AdS$_4$. In particular, taking the flat space limit of the bulk corresponds to taking the speed of light $c$ to zero in the boundary, giving rise to a Carrollian superconformal theory. This limit is subtle to implement for fermions, however, since the Dirac algebra is sensitive to the spacetime metric and therefore takes a different form in Carrollian spacetimes than it does in Minkowski space. In fact, we show that there are four possible ways of realising Carrollian fermions, one of which arises at leading order in the $c\rightarrow0$ limit of relativistic fermions. In three dimensions, there is an additional complication that the minimal realisation of the Carrollian Dirac algebra requires $4\times4$ matrices rather than $2\times 2$ matrices familiar from the relativistic case. Nevertheless, we show that the $c\rightarrow0$ limit of the ABJM theory can be recast in terms of Carrollian Dirac matrices and enjoys and infinite-dimensional Carrollian superconformal symmetry whose bosonic subsector is the extended BMS$_4$ algebra encoding the asymptotic symmetries of four dimensional Minkowski space. This provides a concrete starting point for constructing a Carrollian gauge theory dual to M-theory in flat space.