The maximal D=4 supergravities

Abstract

All maximal supergravities in four space-time dimensions are presented. The ungauged Lagrangians can be encoded in an E_7(7)\Sp(56,R)/GL(28) matrix associated with the freedom of performing electric/magnetic duality transformations. The gauging is defined in terms of an embedding tensor which encodes the subgroup of E_7(7) that is realized as a local invariance. This embedding tensor may imply the presence of magnetic charges which require corresponding dual gauge fields. The latter can be incorporated by using a recently proposed formulation that involves tensor gauge fields in the adjoint representation of E_7(7). In this formulation the results take a universal form irrespective of the electric/magnetic duality basis. We present the general class of supersymmetric and gauge invariant Lagrangians and discuss a number of applications.

41 pages, v2: minor corrections, published version

References in corpus (22)

• A Geometry for Non-Geometric String Backgrounds
• Nongeometric Flux Compactifications
• On Lagrangians and Gaugings of Maximal Supergravities
• Maximal gauged supergravity in three dimensions
• Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
• Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions
• Gauged N=4 supergravities
• The maximal D=5 supergravities
• Magnetic charges in local field theory
• Gauging of Flat Groups in Four Dimensional Supergravity
• The maximal D=7 supergravities
• Gauged supergravity algebras from twisted tori compactifications with fluxes
• Flux Compactifications of M-Theory on Twisted Tori
• N=8 gaugings revisited: an exhaustive classification
• The Scherk-Schwarz mechanism as a flux compactification with internal torsion
• Maximal Supergravity from IIB Flux Compactifications
• Duality and Spontaneously Broken Supergravity in Flat Backgrounds
• Gauging Maximal Supergravities
• Electric-Magnetic Duality in Supergravity
• New Gauged N=8, D=4 Supergravities
• E_{7(7)} symmetry and dual gauge algebra of M-theory on a twisted seven-torus
• Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

Cited by in corpus (126)

• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory II: E${}_{7(7)}$
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Evidence for a family of SO(8) gauged supergravity theories
• Duality orbits of non-geometric fluxes
• The string origin of dyonic $\mathcal{N}=8$ supergravity and its simple Chern-Simons duals
• Gauged Supergravities, Tensor Hierarchies, and M-Theory
• Extended geometry and gauged maximal supergravity
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Gauged Supergravities
• On the vacua of N = 8 gauged supergravity in 4 dimensions
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• The maximal D=7 supergravities
• Generalised geometry for string corrections
• Exceptional field theory: $SL(5)$
• Dyonic ISO(7) supergravity and the duality hierarchy
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Supergravities without an Action: Gauging the Trombone
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• The N>2 supersymmetric AdS vacua in maximal supergravity
• Type II origin of dyonic gaugings
• Multiple Membranes from Gauged Supergravity
• Kaluza-Klein Spectrometry from Exceptional Field Theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• The Gaugings of Maximal D=6 Supergravity
• The SU(3)-invariant sector of new maximal supergravity
• On Type IIB moduli stabilization and N = 4, 8 supergravities
• Generalised Scherk-Schwarz reductions from gauged supergravity
• N=8 Supergravity with Local Scaling Symmetry
• The tensor hierarchy algebra
• How to halve maximal supergravity
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Fourteen new stationary points in the scalar potential of SO(8)-gauged N=8, D=4 supergravity
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• Electric and magnetic charges in N=2 conformal supergravity theories
• Gauging hidden symmetries in two dimensions
• Tensor hierarchies, Borcherds algebras and E11
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• On new maximal supergravity and its BPS domain-walls
• E7(7) invariant Lagrangian of d=4 N=8 supergravity
• N=4 Supersymmetric AdS5 Vacua and their Moduli Spaces
• SO(8) Supergravity and the Magic of Machine Learning
• Exceptional Flux Compactifications
• $P$ fluxes and exotic branes
• Non-linear Kaluza-Klein theory for dual fields
• An $\omega$ Deformation of Gauged STU Supergravity
• Weak gravity versus scale separation
• On the Magical Supergravities in Six Dimensions
• Tachyonic Kaluza-Klein modes and the AdS swampland conjecture
• The complete $D=11$ embedding of SO(8) supergravity
• Lagrangians with electric and magnetic charges of N=2 supersymmetric gauge theories
• $\mathcal{N}=2$ supersymmetric S-folds
• An $\mathcal{N}=3$ Solution in Dyonic ISO(7) Gauged Maximal Supergravity and Its Uplift to Massive Type IIA
• Global Properties of the Conformal Manifold for S-Fold Backgrounds
• The Holographic Conformal Manifold of 3d $\mathcal{N}=2$ $S$-fold SCFTs
• The unbearable lightness of charged gravitini
• Romans-mass-driven flows on the D2-brane
• Electric/magnetic duality for chiral gauge theories with anomaly cancellation
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• The supersymmetric tensor hierarchy of N=1,d=4 supergravity
• The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions
• S-folds and holographic RG flows on the D3-brane
• Standard Model Fermions and N=8 supergravity
• S-folds and (non-)supersymmetric Janus solutions
• Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules
• On the exceptional generalised Lie derivative for $d\ge 7$
• D=4, N=2 Gauged Supergravity coupled to Vector-Tensor Multiplets
• Flat deformations of type IIB S-folds
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Introductory Lectures on Extended Supergravities and Gaugings
• Integrable Scalar Cosmologies II. Can they fit into Gauged Extended Supergavity or be encoded in N=1 superpotentials?
• A note on smeared branes in flux vacua and gauged supergravity
• A Note on E11 and Three-dimensional Gauged Supergravity
• Embedding the SU(3) sector of SO(8) supergravity in $D=11$
• Non-geometric Calabi-Yau Backgrounds and K3 automorphisms
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Ten-dimensional origin of Minkowski vacua in $\mathcal{N}=8$ supergravity
• Gaugings of four-dimensional N=3 supergravity and AdS4/CFT3 holography
• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• Can (Electric-Magnetic) Duality Be Gauged?
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• Gaugings from E7 Extended Geometries
• Maximally Supersymmetric AdS Solutions and their Moduli Spaces
• Exceptional Reductions
• Locally non-geometric fluxes and missing momenta in M-theory
• Correlation Functions in $\omega$-Deformed N=6 Supergravity
• Deformations of vector-scalar models
• Super-Chern-Simons spectra from Exceptional Field Theory
• Universal properties of Kaluza-Klein gravitons
• Critical points of maximal D=8 gauged supergravities
• Constructing black hole solutions in supergravity theories
• Kaluza-Klein Spectrometry beyond Consistent Truncations: The Squashed $S^7$
• Actions for Non-Abelian Twisted Self-Duality
• Leibniz-Yang-Mills Gauge Theories and the 2-Higgs Mechanism
• Supersymmetric solutions from N=6 gauged supergravity
• All maximal gauged supergravities with uplift
• Halving ISO(7) supergravity
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• New AdS${}_4$ Vacua in Dyonic ISO(7) Gauged Supergravity
• Maximal D=2 supergravities from higher dimensions
• Exact holographic RG flows in extended SUGRA
• Vacua Analysis in Extended Supersymmetry Compactifications
• The dual graviton in duality covariant theories
• Attractors, black objects, and holographic RG flows in 5d maximal gauged supergravities
• Twisted compactifications of 6D field theories from maximal 7D gauged supergravity
• Vacua of $\omega$-deformed SO(8) supergravity
• Positive mass theorem in extended supergravities
• Hypermultiplet gaugings and supersymmetric solutions from 11D and massive IIA supergravity on H${}^{(p,q)}$ spaces
• On the U(1)${}^2$-invariant sector of dyonic maximal supergravity
• Supersymmetric solutions of 7D maximal gauged supergravity
• Old and new vacua of 5D maximal supergravity
• Positive energy and non-SUSY flows in ISO(7) gauged supergravity
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• Maximal Nine Dimensional Supergravity, General gaugings and the Embedding Tensor
• Notophs of N = 8 supergravity
• Space-filling branes & gaugings
• Inflation in maximal gauged supergravities
• Holographic 3d $\mathcal{N}=1$ Conformal Manifolds
• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• The very-extended trombone
• Consistent truncations from the geometry of sphere bundles
• Non-Abelian Electric-Magnetic Duality with Supersymmetry in 4D and 10D
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Duality phases and halved maximal D=4 supergravity
• $\mathcal{N}=1$ S-fold spectroscopy