Contractions of AdS brane algebra and superGalileon Lagrangians

TL;DR

This paper explores the derivation of various Galileon Lagrangians from AdS brane algebra contractions, clarifying their invariant forms and supersymmetric extensions using Maurer-Cartan equations and supercosets.

Contribution

It introduces a unified method to obtain flat, non-relativistic, and supersymmetric Galileon Lagrangians via algebra contractions and Maurer-Cartan form analysis.

Findings

Derived DBI, Newton-Hoock, and Galilean Galileons from AdS algebra contractions.

Clarified the role of invariant forms and Wess-Zumino terms in Galileon Lagrangians.

Constructed supersymmetric extensions and identified their relation to bosonic Galileons.

Abstract

We examine AdS Galileon Lagrangians using the method of non-linear realization. By contractions 1) flat curvature limit and 2) non-relativistic brane algebra limit and 3) (1)+(2) limits we obtain DBI, Newton-Hoock and Galilean Galileons respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino terms using Maurer-Cartan equations on the coset $G/SO(3,1)$. We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using SU(2,2|1)/(SO(3,1)x U(1)) supercoset and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates of for supersymmetric Galileon.