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Title of Journal: J High Energ Phys

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Abbravation: Journal of High Energy Physics

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Springer Berlin Heidelberg

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DOI

10.1007/b95112_10

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1029-8479

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Borcherds and KacMoody extensions of simple finit

Authors: Jakob Palmkvist
Publish Date: 2012/06/01
Volume: 2012, Issue: 6, Pages: 3-
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Abstract

We study the Borcherds superalgebra obtained by adding an odd fermionic null root to the set of simple roots of a simple finitedimensional Lie algebra We compare it to the KacMoody algebra obtained by replacing the odd null root by an ordinary simple root and then adding more simple roots such that each node that we add to the Dynkin diagram is connected to the previous one with a single line This generalizes the situation in maximal supergravity where the E n symmetry algebra can be extended either to a Borcherds superalgebra or to the KacMoody algebra E 11 and both extensions can be used to derive the spectrum of pform potentials in the theory We show that also in the general case the Borcherds and KacMoody extensions lead to the same ‘pform spectrum’ of representations of the simple finitedimensional Lie algebra

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