Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics

TL;DR

This work constructs non-relativistic $p$-brane algebras $NH_{\pm}$ in $d$ dimensions as contractions of $dS/AdS$ algebras, and realizes non-relativistic $(p+1)$-branes as Wess-Zumino terms via non-linear coset methods, exploiting non-trivial $p+2$ Eilenberg-Chevalley cohomology. It introduces non-central extensions through vector-valued 2-forms, derives generalized pp-wave metrics from quadratic $H$-invariants, and shows that extended $NH$ algebras embed as subalgebras of the multi-temporal conformal group $SO(d+1,p+2)$. The results connect non-relativistic brane dynamics with cohomological structure and generalized spacetime geometries, including spaces with more than one time coordinate, and may illuminate decoupled sectors in AdS/CFT and potential two-time physics scenarios. Overall, the paper provides a cohesive framework linking algebraic contractions, non-linear realizations, invariant metrics, and higher-dimensional embeddings for non-relativistic branes.

Abstract

The Newton-Hooke algebras in d dimensions are constructed as contractions of dS(AdS) algebras. Non-relativistic brane actions are WZ terms of these Newton-Hooke algebras. The NH algebras appear also as subalgebras of multi-temporal relativistic conformal algebras, SO(d+1, p+2). We construct generalizations of pp-wave metrics from these algebras.