The maximal D = 4 supergravities

By B. Wit, H. Samtleben, Mario Trigiante. 2007

249 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ea882fdbe62d908eea2a3975e4514784776879f1

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Citations in the corpus

M-theory, exceptional generalised geometry and superpotentials (2008, background): “Interestingly such generic supergravities are encoded by an embedding tensor [68] which, like φ, lies in the 912 representation of E7(7).”
Gauged Supergravities. (2016, methodology): “Such terms are given in the maximal and N = 2 theories in [111, 121] and [126], respectively.”
Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, background): “in the embedding tensor formulation of gauged supergravities [38], including gaugings [39] of the so-called “trombone” symmetry [40].”
Double field theory: a pedagogical review (2013, unknown): “2 The E7(7) case and maximal gauged supergravity E7(7) is the U-duality group of gauged maximal supergravity in four dimensions [97], the ungauged theory being obtained through compactifications of M-theory on a seven-torus [98].”
Extended geometry and gauged maximal supergravity (2013, background): “Remarkably, this takes the exact same form as the scalar potential of gauged maximal supergravity [32] if we identify the generalized metric with the moduli space matrix M.”
Magnetic charges in local field theory (2005, background): “Of course, this invariance is only realized provided that also the field equations associated with fields other than the gauge fields, will respect the invariance.”
Lectures on gauged supergravity and flux compactifications (2008, background): “56 912 6480 : (3.8) Compatibility of the deformation with supersymmetry can be expressed in an E 7(7)- covariant way and restricts the embedding tensor to the 912 representation in this decomposition [13, 42]. I.e. as a matrix M has only 912 linearly independent entries. We will sketch the argument ”
Exceptional field theory. II. E$_{7(7)}$ (2013, methodology): “s FµνM and thereby the twisted ﬁrst-order selfduality equations (3.7) and the action (1.4). Again, this counting is in precise agreement with 18 the general structure of maximal gauged supergravities [14]: the existence of non-abelian selfduality equations requires a compensating 2-form per vector ﬁ”
Gauged Supergravities, Tensor Hierarchies, and M-Theory (2008, background): “H µν N⌋|| +2Λ⌈||MX µν N⌋|| +2A [µ ⌈||M δ(Λ)A ν] N⌋|| = 2eεµνρ Λ⌈||MVN⌋||A PρA +2A[µ⌈||M δ(Λ)Aν]N⌋|| . (5.25) This deformation is reminiscent of what happens, for instance, in D= 4 gauged supergravity [38, 26, 17], where the two-form ﬁelds acquire also additional variations once they couple to other ”
Duality orbits of non‐geometric fluxes (2012, background): “In particular, in the context of half-maximal [1] and maximal [2] gauged supergravities, not only does supersymmetry tightly organise the ungauged theory, but also it strictly determines the set of possible deformations (i.”