Schreiber Lie n-algebras of BPS charges

An article that we have written:

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• Hisham Sati, Urs Schreiber

  Lie $n$-algebras of BPS charges

  J. High Energ. Phys. (2017) 2017: 87.

  (arXiv:1507.08692, DOI: 10.1007/JHEP03(2017)087 , talk slides)

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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.

See also the companion articles

• The WZW term of the M5-brane

• Lie n-algebras of higher Noether currents

Lecture notes are at

• Structure Theory for Higher WZW Terms

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