Chiral and Real N=2 supersymmetric l-conformal Galilei algebras

Abstract

Inequivalent N=2 supersymmetrizations of the l-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2,2) and the real (1,2,1) basic supermultiplets of the N=2 supersymmetry. For non-negative integer and half-integer l both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N=2 case coincides with the superalgebra introduced by Masterov, while the chiral N=2 case is a new superalgebra. We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer l and the other only for d=2 and integer l. For each central extension the centrally extended l-superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators.

14 pages

References in corpus (13)

• Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry
• Galilean Superconformal Symmetries
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Supersymmetric Extension of Galilean Conformal Algebras
• Supersymmetric Extension of GCA in 2d
• Nonrelativistic conformal groups and their dynamical realizations
• D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• N=2 supersymmetric extension of l-conformal Galilei algebra
• The algebraic structure of Galilean superconformal symmetries
• N = 2 Galilean superconformal algebras with central extension
• Nonrelativistic conformal transformations in Lagrangian formalism
• N-Galilean conformal algebras and higher derivatives Lagrangians

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• Super-GCA from $\mathcal{N}=(2,2)$ Super-Virasoro
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of $\mathcal{N}=2$ super Schrödinger algebras and their representations
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of $\mathcal{N}=1$ superconformal Galilei algebras and their representations
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• New realizations of N=2 l-conformal Newton-Hooke superalgebra
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• Superfield approach to higher derivative N=1 superconformal mechanics
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• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• New constrained generalized Killing spinor field classes in warped flux compactifications