Nonrelativistic expansion of M2 branes and M theory backgrounds

TL;DR

This paper develops a systematic framework for analyzing nonrelativistic M2 brane solutions in M theory using 11d membrane Newton-Cartan geometry and a 1/c expansion, revealing that nontrivial dynamics emerge beyond leading order.

Contribution

It introduces a novel approach combining 11d membrane Newton-Cartan geometry with a 1/c expansion to study nonrelativistic M2 branes, highlighting the order at which dynamics become nontrivial.

Findings

Leading order action is trivial for certain embeddings.

Nontrivial dynamics appear at next-to-leading order and beyond.

Derived dispersion relations for nonrelativistic M2 brane configurations.

Abstract

We initiate a systematic analysis of the nonrelativistic membrane solutions of M theory using the notion of 11d membrane Newton-Cartan (MNC) geometry as well as considering a $ 1/c^2 $ expansion for the embedding fields of the M2 brane world-volume theory. We discuss the associated boost and dilatation symmetries of the nonrelativistic world-volume theory at leading order in the $ 1/c $ expansion. We show that, in the static gauge, when the world-volume directions of the nonrelativistic M2 brane are stretched along the longitudinal axes of the target space geometry, the leading order action in the $ 1/c $ expansion becomes trivial. In other words, the nontrivial dynamics appears to be only at NLO and beyond. In our analysis, we focus on such embeddings only and obtain the corresponding dispersion relation associated with the nonrelativistic world-volume theory.