Affine Extension of Galilean Conformal Algebra in 2+1 Dimensions

Abstract

We show that a class of nonrelativistic algebras including non centrally-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 plain. We suggest that this affine form may be the symmetry that explains the relaxation of some classical phenomena towards 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 AdS theory. This suggests that AdS/CFT duality may take on a special form in four dimensions.

arXiv comment13 pages, no figures. Some references added, typos corrected, minor changes in content

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