Non-Lorentzian Field Theories with Maximal Supersymmetry and Moduli Space Dynamics

TL;DR

This paper introduces non-Lorentzian gauge theories with maximal supersymmetry in 2+1 and 4+1 dimensions, modeling boosted M-branes with dynamics confined to moduli spaces of BPS states.

Contribution

It constructs new gauge theories invariant under rotations and translations but not boosts, capturing the dynamics of infinitely boosted M2- and M5-branes with reduced supersymmetry.

Findings

Theories describe M-branes with null worldvolume time.

Dynamics reduce to motion on BPS moduli spaces.

Half the supersymmetry is realized on each moduli space component.

Abstract

We present gauge theories in 2+1 and 4+1 dimensions with 16 supersymmetries which are invariant under rotations and translations but not boosts. The on-shell conditions reduce the dynamics to motion on a moduli space of BPS states graded by a topologically conserved quantity. On each component of the moduli space only half the supersymmetry is realised. We argue that these theories describe M2-branes and M5-branes which have been infinitely boosted so that their worldvolume `time' has become null.