Lie n-algebras of BPS charges

TL;DR

This paper reveals higher algebraic structures, specifically Lie (p+1)-algebras, on BPS charges and Noether currents in super p-brane models, providing a refined mathematical framework for M-brane charges in M-theory.

Contribution

It introduces a super Lie (p+1)-algebra framework for BPS charges, extending traditional Lie algebra structures to higher algebraic contexts in superstring and M-theory models.

Findings

Higher algebraic structures on Noether currents and BPS charges.

Refinement of BPS charge extensions using super Lie (p+1)-algebras.

Cohomological corrections suggest M-brane charges reside in twisted cohomology.

Abstract

We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.