2012
DOI: 10.1007/jhep04(2012)078
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E 11, Borcherds algebras and maximal supergravity

Abstract: 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 V 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… Show more

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Cited by 29 publications
(69 citation statements)
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“…Our main result is presented in section 3.1, where we show that the tensors defining the hierarchy can be interpreted as elements in the Borcherds algebra. In section 3.2 we show that the Borcherds algebras and E 11 lead to the same p-form representations in the level decompositions up to p = D (which has been explained differently in [13]), and for arbitrarily large p if E 11 is replaced by E r with sufficiently large rank r. We conclude the paper in section 4.…”
Section: Introductionmentioning
confidence: 83%
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“…Our main result is presented in section 3.1, where we show that the tensors defining the hierarchy can be interpreted as elements in the Borcherds algebra. In section 3.2 we show that the Borcherds algebras and E 11 lead to the same p-form representations in the level decompositions up to p = D (which has been explained differently in [13]), and for arbitrarily large p if E 11 is replaced by E r with sufficiently large rank r. We conclude the paper in section 4.…”
Section: Introductionmentioning
confidence: 83%
“…Another way is to embed g into an infinitedimensional Lie (super)algebra, either a Borcherds algebra (which depends on g) or the indefinite Kac-Moody algebra E 11 . In the level decomposition of the Borcherds algebra with respect to g, the representation content on level p coincides with r p , up to level D − 2 [4,12,13]. The same is true for E 11 if the level decomposition is done with respect to g ⊕ sl D , and restricted to tensors that are antisymmetric under sl D [14][15][16][17][18][19].…”
Section: Introductionmentioning
confidence: 87%
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