Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity

Abstract

We study properties of D = 4, N >1 extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity. This involves a detailed classification of the "degenerations" of the duality groups of type E7, when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G4 "degenerates" into a perfect square. With regard to cosmological applications, we conclude that the consistent truncation to N = 1 from higher-dimensional or higher-N theory gives a zero measure minimal coupling of vectors. A non-minimal coupling involving vectors coupled to scalars and axions is generic. These features of supergravity, following from the electric-magnetic duality, may be useful in other applications, like stabilization of moduli, and in studies of non-perturbative black-hole solutions of supergravity/string theory.

1+40 pages, 5 Tables; v2 : 1+41 pages, Sec. 3 extended, Sec. 3.1 replaced, Sec. 4.3 removed, one Ref. added, other minor changes

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• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Chaotic inflation and supersymmetry breaking
• Exact Attractive Non-BPS STU Black Holes
• Black holes admitting a Freudenthal dual
• Magic Supergravities, N= 8 and Black Hole Composites
• N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• Twin Supergravities
• Creation of Matter in the Universe and Groups of Type E7
• More on N=8 Attractors
• Exceptional Reductions
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Cited by in corpus (32)

• Symplectic Deformations of Gauged Maximal Supergravity
• Twin Supergravities from Yang-Mills Squared
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• New E77 invariants and amplitudes
• Freudenthal Dual Lagrangians
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• N=2 SUGRA BPS Multi-center solutions, quadratic prepotentials and Freudenthal transformations
• Freudenthal Gauge Theory
• On Extremal Limits and Duality Orbits of Stationary Black Holes
• Dualities Near the Horizon
• On Absence of 3-loop Divergence in N=4 Supergravity
• Black holes and equivariant charge vectors in N=2,d=4 supergravity
• The Action with Manifest E7 Type Symmetry
• Nonlinear symmetries of black hole entropy in gauged supergravity
• Black holes and general Freudenthal transformations
• Black Holes and Higher Composition Laws
• Orbits in Non-Supersymmetric Magic Theories
• D = 3 Unification of Curious Supergravities
• Quarter-BPS Black Holes in AdS${}_4$-NUT from $N=2$ Gauged Supergravity
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
• The supersymmetric black holes of N=8 supergravity
• Smarr Mass formulas for BPS multicenter Black Holes
• Extremal Black Holes, Stueckelberg Scalars and Phase Transitions
• Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
• Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification
• Multi-Centered Invariants, Plethysm and Grassmannians
• Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
• Exceptional Periodicity and Magic Star Algebras. I : Foundations
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• Jordan meets Freudenthal. A Black Hole Exceptional Story
• Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations
• Gaugings and other aspects in supergravity