Affine extension of Galilean conformal algebra in 2+1 dimensions

We show that a class of nonrelativistic algebras including noncentrally extended Schrodinger algebra and Galilean conformal algebra (GCA) has an affine extension in 2+1 hitherto unknown. This extension arises out of the conformal symmetries of the two dimensional complex plane. We suggest that this affine form may be the symmetry that explains the relaxation of some classical phenomena toward their critical point. This affine algebra admits a central extension and maybe realized in the bulk. The bulk realization suggests that this algebra may be derived by looking at the asymptotic symmetry of an Anti-de Sitter (AdS) theory. This suggests that AdS/CFT (conformal field theory) duality may take on a special form in four dimensions. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3371191]