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

TL;DR

This paper formalizes higher gauge WZW sigma-models using super Lie n-algebra homotopy theory, revealing the algebraic structure of super p-branes and their condensates in string/M-theory, including dualities and non-perturbative aspects.

Contribution

It introduces a super Lie n-algebra framework to describe super p-branes, brane condensates, and dualities, unifying various brane spectra and non-perturbative effects in string/M-theory.

Findings

Realizes super p-brane spectrum via super Lie n-algebra homotopy theory

Provides algebraic proof of spacetime equivalences and dualities

Describes non-perturbative sigma-models with higher WZW terms

Abstract

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 sigma-model branes (open brane ending on background brane) are encoded precisely in (super-) L-infinity-extension theory and how the resulting "extended (super-)spacetimes" formalize spacetimes containing sigma 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 sigma-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 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 11-dimensional 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 sigma-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.