The M5-Brane Limit of Eleven-Dimensional Supergravity

TL;DR

This work constructs the M5-brane limit of eleven-dimensional supergravity, yielding a non-relativistic action invariant under Galilean boosts and a local dilatation symmetry. A Hubbard–Stratonovich transformation reveals Lagrange multipliers that enforce two key constraints, and a Poisson-type equation arises from subleading terms in the relativistic equations of motion, supplying the missing dynamical content. The limit describes gravitational fluctuations around a stack of M5-branes in a flat Minkowski background, with the M5-brane number N_M5 fixed by flux of the Lagrange multiplier through the transverse sphere. The duality relations and the Einstein equation are shown to reduce to consistent, covariant constraints and a Poisson equation, respectively, ensuring a complete non-relativistic dynamics. The results open avenues for exploring non-relativistic brane limits, potential dualities, and holographic connections without relying on AdS factors.

Abstract

We construct the M5-brane limit of eleven-dimensional supergravity. The resulting action is invariant under Galilean boosts and has a local scale symmetry. We also consider the limit of the equations of motion where we recover a Poisson-like equation arising from an M5-brane source but which does not follow from the non-relativistic action. We argue that the resulting theory describes gravitational fluctuations around a stack of M5-branes, represented by a trivial Minkowskian spacetime, but where the number of M5-branes is determined by the flux of a Lagrange multiplier field.