Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity

Abstract

We investigate the conjectured infinite-dimensional hidden symmetries of six-dimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the $F_{4,4}$ symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space $F_{4,4}^{++}/K(F_{4,4}^{++})$ using the level decomposition associated with the subalgebra $\mathfrak{gl}(5)\oplus \mathfrak{sl}(2)$ of $F_{4,4}^{++}$ and show their equivalence with the bosonic equations of motion of six-dimensional chiral supergravity up to the level where the dual graviton appears. In particular, the self-duality condition on the chiral $2$-form is automatically implemented in the sense that no dual potential appears for that $2$-form, in contradistinction with what occurs for the non chiral $p$-forms. (ii) Second, we describe the $p$-form hierarchy of the model in terms of its $V$-duality Borcherds superalgebra, of which we compute the Cartan matrix.

31 pages. v2: Error in section 6.3 corrected, Dynkin diagram now appears correctly, minor typos

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• E_7(7) on the Light Cone
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• Duality Symmetries and G^{+++} Theories
• E8(8) in Light Cone Superspace

Cited by in corpus (1)

• Forms and algebras in (half-)maximal supergravity theories