Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields - INSPIRE

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Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields

Aug 23, 2013

35 pages

Published in:

Int.J.Geom.Meth.Mod.Phys. 12 (2014) 1550018

Published: Dec 11, 2014

e-Print:

1308.5264 [hep-th]

DOI:

10.1142/S0219887815500188

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Abstract: (World Scientific)

We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L

_{∞}

-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

Note:

28 pages, published version plus one typo fixed

Lie n-algebras
Lie superalgebras
p-branes
WZW model
multiplet: tensor
algebra: Lie
membrane model
sigma model
space-time
condensation

References(52)

Figures(0)

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