Lie n-algebras of BPS charges

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.

19 pages, v2: references added, details of the main computation spelled out

References in corpus (3)

• The WZW term of the M5-brane and differential cohomotopy
• An approach to anomalies in M-theory via KSpin
• Topological BPS charges in 10 and 11-dimensional supergravity

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• Higher prequantum geometry
• On the hidden symmetries of $D=11$ supergravity
• Super Cartan geometry and the super Ashtekar connection
• Supersymmetric minisuperspace models in self-dual loop quantum cosmology
• Geometric supergravitty
• Supergravities and Branes from Hilbert-Poincaré Series
• Field Theory via Higher Geometry I: Smooth Sets of Fields
• Brane current algebras and generalised geometry from QP manifolds
• The Hidden M-Group
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces