Mathcal{N} = 1, 2, 3 \u2113-conformal Galilei superalgebras

Anton Galajinsky,Ivan Masterov

doi:10.1007/jhep08(2021)165

Abstract

The issue of constructing mathcal{N} = 1, 2, 3 supersymmetric extensions of the ℓ-conformal Galilei algebra is reconsidered following the approach in [27]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d = 1, mathcal{N} -extended superconformal group, a new mathcal{N} = 1 ℓ-conformal Galilei superalgebra, two new mathcal{N} = 2 variants, and two new mathcal{N} = 3 versions are built. Realisations in terms of differential operators in superspace are given.

Highlights

In modern literature, the reciprocal of is called the rational dynamical exponent and (1.1) is sometimes referred to as the conformal Galilei algebra with rational dynamical exponent
If the tower of acceleration generators is reduced to a single spatial translation generator, the special conformal transformations are discarded, and the dynamical exponent is regarded arbitrary, one recovers the so called Lifshitz algebra
The Lifshitz holography has interesting peculiarities and it has been extensively studied in the past

Summary

Introduction

The reciprocal of is called the rational dynamical exponent and (1.1) is sometimes referred to as the conformal Galilei algebra with rational dynamical exponent. = 1, known as the Schrodinger algebra and the conformal Galilei algebra, have received the utmost attention (for a review see [10]). If the tower of acceleration generators is reduced to a single spatial translation generator, the special conformal transformations are discarded, and the dynamical exponent is regarded arbitrary, one recovers the so called Lifshitz algebra. When constructing a specific dynamical realisation of a non-relativistic conformal group, generators of the corresponding Lie algebra are linked to constants of the motion. Because the number of functionally independent integrals of motion needed to integrate a differential equation correlates with its order, dynamical realisations of an

Objectives

Conclusion