Super Galilean conformal algebra in AdS/CFT

TL;DR

This paper explores the relationship between Galilean conformal algebra (GCA) and Newton-Hooke string algebra within the AdS/CFT framework, revealing how GCA emerges as a boundary realization of the bulk algebra and deriving supersymmetric extensions.

Contribution

It demonstrates that GCA is a boundary realization of the Newton-Hooke string algebra in AdS space and derives various supersymmetric GCAs from superconformal algebras.

Findings

GCA is a boundary realization of Newton-Hooke string algebra in AdS.

32 supersymmetric GCAs are derived from superconformal algebras.

Less supersymmetric GCAs are also constructed.

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).