Super Galilean conformal algebra in AdS/CFT

TL;DR

The paper demonstrates that the Galilean conformal algebra ($GCA$) is the boundary realization of the Newton–Hooke string algebra in AdS, obtained by an Inönü–Wigner contraction of the conformal (and AdS) algebras. It constructs a broad family of supersymmetric GCAs by contracting four-, three-, and six-dimensional superconformal algebras, yielding 32-, 16-, and 8–supercharge GCAs, as well as their semi-GCA variants, each corresponding to specific AdS brane configurations with AdS$_2$–, AdS$_2\times$S$^1$, or AdS$_3$ worldvolumes. The results provide a concrete NR holographic framework linking boundary GCAs to bulk NH algebras for branes in AdS backgrounds, with explicit projector-based contractions and brane interpretations. These constructions illuminate the role of brane geometry in NR symmetries and open avenues for exploring NR CFTs and their holographic duals, including potential connections to Newton-Cartan-like geometries and central extensions.

Abstract

Galilean conformal algebra (GCA) is an Inonu-Wigner (IW) contraction of a conformal algebra, while Newton-Hooke string algebra is an IW contraction of an AdS algebra which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton-Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS_2. The one-dimensional conformal symmetry so(2,1) and rotational symmetry so(d) contained in the GCA are realized as the symmetry on the AdS_2 string worldsheet and rotational symmetry in the space transverse to the AdS_2 in AdS_{d+2}, respectively. It follows from this correspondence that 32 supersymmetric GCAs can be derived as IW contractions of superconformal algebras, psu(2,2|4), osp(8|4) and osp(8^*|4). We also derive less supersymmetric GCAs from su(2,2|2), osp(4|4), osp(2|4) and osp(8^*|2).