N=8 gaugings revisited: an exhaustive classification

Abstract

In this paper we reconsider, for N=8 supergravity, the problem of gauging the most general electric subgroup. We show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding of the gauge group G within the electric subalgebra SL(8,\IR) of E_{7(7)}. The complete set of solutions to this equation contains 36 parameters. Modding by the action of SL(8,\IR) conjugations that yield equivalent theories all continuous parameters are eliminated except for an overall coupling constant and we obtain a discrete set of orbits. This set is in one--to--one correspondence with 36 Lie subalgebras of SL(8,\IR), corresponding to all possible real forms of the SO(8) Lie algebra plus a set of contractions thereof. By means of our analysis we establish the theorem that the N=8 gaugings constructed by Hull in the middle eighties constitute the exhaustive set of models. As a corollary we show that there exists a unique 7--dimensional abelian gauging. The corresponding abelian algebra is not contained in the maximal abelian ideal of the solvable Lie algebra generating the scalar manifold E_{7(7)}/SU(8).

arXiv comment1 LaTeX file, 41 pages, 3 eps-figures

References in corpus (18)

• String Theory Dynamics In Various Dimensions
• Heterotic and Type I String Dynamics from Eleven Dimensions
• Unity of Superstring Dualities
• N=2 Extremal Black Holes
• Black Holes and Critical Points in Moduli Space
• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Vacuum interpolation in supergravity via super p-branes
• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• Microscopic Entropy of N=2 Extremal Black Holes
• Spontaneous Breaking of N=2 to N=1 in Rigid and Local Supersymmetric Theories
• Minimal Higgs Branch for the Breaking of Half of the Supersymmetries in N=2 Supergravity
• Enhancement of Supersymmetry Near 5d Black Hole Horizon
• R--R Scalars, U--Duality and Solvable Lie Algebras
• Solvable Lie Algebras in Type IIA, Type IIB and M Theories
• E_{7(7)} Duality, BPS Black-Hole Evolution and Fixed Scalars
• Spontaneous N=2 --> N=1 local supersymmetry breaking with surviving local gauge group
• Supermembranes with fewer supersymmetries
• Superpotential from Black Holes

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