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.

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

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• Supersymmetric Extension of GCA in 2d
• Topologically Massive Gravity and Galilean Conformal Algebra: A Study of Correlation Functions
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Dynamical symmetries and causality in non-equilibrium phase transitions
• Super-GCA from $\mathcal{N}=(2,2)$ Super-Virasoro
• Logarithmic Correlators in Non-relativistic Conformal Field Theory
• Galilean contractions of $W$-algebras
• Aspects of Ultra-Relativistic Field Theories via Flat-space Holography
• On Holographic Realization of Logarithmic GCA
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Logarithmic Exotic Conformal Galilean Algebras
• Physical ageing and new representations of some Lie algebras of local scale-invariance
• Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1
• Semi-classical BMS-blocks from the Oscillator Construction
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Higher-order Galilean contractions
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• Multi-graded Galilean conformal algebras
• Asymmetric Galilean conformal algebras
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Galilean $W_3$ algebra
• Fractional Galilean Symmetries