Galilean Conformal and Superconformal Symmetries

TL;DR

This paper explores various nonrelativistic conformal algebras, especially the Galilean conformal algebra (GCA), derived from relativistic conformal algebra through contraction limits, and extends to superconformal symmetries.

Contribution

It provides a detailed analysis of the Galilean conformal algebra and its superconformal extension obtained via nonrelativistic contraction limits.

Findings

Derivation of GCA from relativistic conformal algebra.

Identification of contraction limits leading to GCA.

Construction of Galilei conformal superalgebra (GCSA).

Abstract

Firstly we discuss briefly three different algebras named as nonrelativistic (NR) conformal: Schroedinger, Galilean conformal and infinite algebra of local NR conformal isometries. Further we shall consider in some detail Galilean conformal algebra (GCA) obtained in the limit c equal to infinity from relativistic conformal algebra O(d+1,2) (d - number of space dimensions). Two different contraction limits providing GCA and some recently considered realizations will be briefly discussed. Finally by considering NR contraction of D=4 superconformal algebra the Galilei conformal superalgebra (GCSA) is obtained, in the formulation using complex Weyl supercharges.