Non-Relativistic AdS Branes and Newton-Hooke Superalgebra

TL;DR

This work establishes a systematic non-relativistic (NR) framework for D-branes in AdS$_5\times$S$^5$ and M-branes in AdS$_{4/7}\times$S$^{7/4}$ by deriving Newton–Hooke (NH) superalgebras as Inönü–Wigner contractions of the AdS$\times$S superalgebras. It classifies admissible branes through compatibility of the worldvolume isometry with the transverse Lorentz symmetry, yielding constrained brane configurations that admit NH superalgebras, and it extends this construction to IIB/M pp-waves. The Wess–Zumino terms are analyzed via Chevalley–Eilenberg cohomology on the relevant superalgebras, identifying non-trivial CE classes (except for certain flat-string cases) and enabling the non-relativistic expansion of brane actions. The NR AdS brane actions are derived for D$p$ (with specified parity conditions) and M2/M5 branes, revealing flux-induced corrections and gauge-fixed simplifications that reproduce known flat-space limits. Overall, the paper provides a unified, cohomology-grounded, NR description of AdS branes across IIA/IIB and M-theory, clarifying the bridge to pp-wave limits and offering a foundation for further solvable NR subsectors in holography.

Abstract

We examine a non-relativistic limit of D-branes in AdS_5xS^5 and M-branes in AdS_{4/7}xS^{7/4}. First, Newton-Hooke superalgebras for the AdS branes are derived from AdSxS superalgebras as Inonu-Wigner contractions. It is shown that the directions along which the AdS-brane worldvolume extends are restricted by requiring that the isometry on the AdS-brane worldvolume and the Lorentz symmetry in the transverse space naturally extend to the super-isometry. We also derive Newton-Hooke superalgebras for pp-wave branes and show that the directions along which a brane worldvolume extends are restricted. Then the Wess-Zumino terms of the AdS branes are derived by using the Chevalley-Eilenberg cohomology on the super-AdSxS algebra, and the non-relativistic limit of the AdS-brane actions is considered. We show that the consistent limit is possible for the following branes: Dp (even,even) for p=1 mod 4 and Dp (odd,odd) for p=3 mod 4 in AdS_5xS^5, and M2 (0,3), M2 (2,1), M5 (1,5) and M5 (3,3) in AdS_{4}xS^{7} and S^{4}xAdS_{7}. We furthermore present non-relativistic actions for the AdS branes.