E11, Borcherds algebras and maximal supergravity View Full Text


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Article Info

DATE

2012-04

AUTHORS

Marc Henneaux, Bernard L. Julia, Jérôme Levie

ABSTRACT

The dynamical p-forms of torus reductions of maximal supergravity theory have been shown some time ago to possess remarkable algebraic structures. The set (“dynamical spectrum”) of propagating p-forms has been described as a (truncation of a) real Borcherds superalgebra D that is characterized concisely by a Cartan matrix which has been constructed explicitly for each spacetime dimension 11 ≥ D ≥ 3. In the equations of motion, each differential form of degree p is the coefficient of a (super-) group generator, which is itself of degree p for a specific gradation (the -gradation). A slightly milder truncation of the Borcherds superalgebra enables one to predict also the “spectrum” of the non-dynamical (D − 1) and D-forms. The maximal supergravity p-form spectra were reanalyzed more recently by truncation of the field spectrum of E11 to the p-forms that are relevant after reduction from 11 to D dimensions. We show in this paper how the Borcherds description can be systematically derived from the split (“maximally non compact”) real form of E11 for D ≥ 1. This explains not only why both structures lead to the same propagating p-forms and their duals for p ≤ (D − 2), but also why one obtains the same (D−1)-forms and “top” D-forms. The Borcherds symmetries 2 and 1 are new too. We also introduce and use the concept of a presentation of a Lie algebra that is covariant under a given subalgebra. More... »

PAGES

78

References to SciGraph publications

  • 2009-04-29. Gauge theories, duality relations and the tensor hierarchy in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-09-11. E11 and the embedding tensor in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-08-20. Einstein billiards and overextensions of finite-dimensional simple Lie algebras in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-02-13. E11-extended spacetime and gauged supergravities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-08-30. IIB supergravity revisited in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-05. IIA/IIB supergravity and ten-forms in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-02-18. Kac-Moody spectrum of (half-)maximal supergravities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-07-13. IIA ten-forms and the gauge algebras of maximal supergravity theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-04-26. Borcherds symmetries in M-theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-07-27. D = 10, N = IIB supergravity in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-07-24. The E11 origin of all maximal supergravities in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/jhep04(2012)078

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    http://dx.doi.org/10.1007/jhep04(2012)078

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    https://app.dimensions.ai/details/publication/pub.1010727127


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