Carrollian superconformal theories and super BMS

TL;DR

This work develops the algebraic backbone of Carrollian superconformal theories in boundary dimensions $d>3$, constructing a finite $ ext{N}=1$ Carrollian CSA via a precise ultra-relativistic contraction and proposing an infinite-dimensional lift that mirrors the expected super-BMS structure. It provides a superspace realization for $ abla ext{N}=1$ CSA, and begins the representation-theory program by examining Carrollian primaries, left/right chiral multiplets, and their transformations under the infinite fermionic towers. The framework is then generalized to higher $\mathcal{N}$, including an $ ext{N}=4$ CSA with extended $R$-symmetry, and the intrinsic multiplet structure is connected to the limiting relativistic theory. Overall, the paper lays the groundwork for flat-space holography with Carrollian supersymmetry and points to future explorations of explicit Carrollian field theories, large-$N$ limits, and bulk-boundary dictionaries.

Abstract

We investigate the supersymmetric versions of Bondi-Metzner-Sachs or, equivalently, conformal Carroll symmetry in boundary dimensions $d>3$, with applications of flat space holography in mind. We identify the contraction of the relativistic symmetry relevant for our purposes and construct a finite-dimensional Carrollian superconformal algebra (CSA) before proposing an infinite-dimensional lift. We provide the superspace formulation for $\mathcal{N}=1$ CSA and work towards an understanding of the representation theory of the algebra. We conclude with some aspects of $\mathcal{N}>1$ CSA.

Figures (1)

• Figure 1: Carrollian chiral multiplet structure