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Lie n-algebras of BPS charges | | Hisham Sati
; Urs Schreiber
; | | Date: |
30 Jul 2015 | | 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. | | Source: | arXiv, 1507.8692 | | Services: | Forum | Review | PDF | Favorites | |
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