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.

arXiv comment31 pages. v2: Error in section 6.3 corrected, Dynkin diagram now appears correctly, minor typos

References in corpus (31)

• A Note on the Green - Schwarz Mechanism in Open - String Theories
• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• Chaos in Superstring Cosmology
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein Models
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Spacelike Singularities and Hidden Symmetries of Gravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• New Couplings of Six-Dimensional Supergravity
• NOTE ON MANIFEST LORENTZ AND GENERAL COORDINATE INVARIANCE IN DUALITY SYMMETRIC MODELS.
• Kac-Moody Symmetries of IIB Supergravity
• The Symmetry of M-Theories
• Tensor and Vector Multiplets in Six-Dimensional Supergravity
• Representations of G+++ and the role of space-time
• Einstein billiards and overextensions of finite-dimensional simple Lie algebras
• Borcherds symmetries in M-theory
• IIB supergravity and E10
• Comments on Chiral p-Forms
• Covariant actions for N=1, D=6 Supergravity theories with chiral bosons
• E_7(7) on the Light Cone
• Consistent and covariant anomalies in six-dimensional supergravity
• Duality invariance implies Poincare invariance
• Constraints and the E10 Coset Model
• Abelian Vectors and Self-Dual Tensors in Six-Dimensional Supergravity
• Symmetry-deforming interactions of chiral p-forms
• Duality Symmetries and G^{+++} Theories
• E8(8) in Light Cone Superspace
• Five-dimensional Supergravity and Hyperbolic Kac-Moody Algebra G2H
• Oxidizing Borcherds symmetries
• Sugawara-type constraints in hyperbolic coset models

Cited by in corpus (2)

• Notes on generalized global symmetries in QFT
• Forms and algebras in (half-)maximal supergravity theories