Freudenthal Dual Lagrangians

Abstract

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial "Polyakov- type" action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.

1+16 pages, 1 Table, updated to match published version

References in corpus (25)

• Charge Orbits of Symmetric Special Geometries and Attractors
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Comments on the Spectrum of CHL Dyons
• Universal BPS structure of stationary supergravity solutions
• Black Holes, Qubits and Octonions
• Strings, Black Holes, and Quantum Information
• Black holes admitting a Freudenthal dual
• The black-hole/qubit correspondence: an up-to-date review
• Orbits and Attractors for N=2 Maxwell-Einstein Supergravity Theories in Five Dimensions
• Three fermions with six single particle states can be entangled in two inequivalent ways
• N=8 Dyon Partition Function and Walls of Marginal Stability
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Partial separability revisited: Necessary and sufficient criteria
• Jordan algebras, exceptional groups, and higher composition laws
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• The Freudenthal gauge symmetry of the black holes of N=2,d=4 supergravity
• U-duality Invariant Dyon Spectrum in type II on T^6
• Hidden symmetries of the Nambu-Goto action
• Extremal Black Holes in Supergravity
• Black Hole Nilpotent Orbits and Tits Satake Universality Classes
• Hitchin functionals are related to measures of entanglement
• Jordan C*-Algebras and Supergravity
• The supersymmetric black holes of N=8 supergravity
• Jordan Algebras and Extremal Black Holes

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• A Kind of Magic
• Black holes and general Freudenthal transformations
• Nonlinear symmetries of black hole entropy in gauged supergravity
• Black Holes and Higher Composition Laws
• Orbits in Non-Supersymmetric Magic Theories
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity
• Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
• Supersymmetric Black Holes and Freudenthal Duality
• Freudenthal Duality in Conformal Field Theory