Affine Extension of Galilean Conformal Algebra in 2+1 Dimensions

TL;DR

This paper introduces an affine extension of the Galilean Conformal Algebra in 2+1 dimensions, revealing new symmetries potentially relevant for understanding critical phenomena and their holographic duals.

Contribution

It uncovers a previously unknown affine extension of nonrelativistic algebras, connecting conformal symmetries in 2D to higher-dimensional nonrelativistic algebras.

Findings

Affine extension of GCA and Schrödinger algebra in 2+1 dimensions identified.

The extended algebra admits a central extension and can be realized in the bulk.

Implications for AdS/CFT duality in four dimensions suggested.

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.