Supersymmetric Extension of Galilean Conformal Algebras

Abstract

The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the co-ordinates in superspace to construct the N=1 Super Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher $N$.

19 pages; v2: 20 pages, Appendix on OPEs added, other minor changes, references added

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• Supersymmetric Extension of GCA in 2d
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• N=2 superconformal Newton-Hooke algebra and many-body mechanics
• Celestial Holography: Lectures on Asymptotic Symmetries
• N = 2 Galilean superconformal algebras with central extension
• Metrics with Galilean Conformal Isometry
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Addendum to "Super-GCA from $\mathcal{N}=(2,2)$ super-Virasoro": Super-GCA connection with tensionless strings
• Galilean Electrodynamics: Covariant formulation and Lagrangian
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• D=4 Extended Galilei Superalgebras with Central Charges
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Asymmetric Galilean conformal algebras
• Free-field construction of Carrollian $W_N$-algebras
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity