Consistent N = 8 $$ \mathcal{N}=8 $$ truncation of massive IIA on S 6

Abstract

Massive type IIA supergravity is shown to admit a consistent truncation on the six-sphere to maximal supergravity in four dimensions with a dyonic ISO(7) gauging. We obtain the complete, non-linear embedding of all the D = 4 fields into the IIA metric and form potentials, and show its consistency. We first rewrite the IIA theory in an SO(1, 3) × SL(7)-covariant way. Then, we employ an N = 8 SL(7)-covariant restriction of the D = 4 tensor hierarchy in order to find the full embedding. The redundant D = 4 degrees of freedom introduced by the tensor hierarchy can be eliminated by writing the embedding in terms of the field strengths and exploiting the restricted duality hierarchy. In particular, closed expressions for the Freund-Rubin term are found using this technique which reveal a pattern valid for other truncations. Finally, we show that the present N = 8 truncation of massive IIA on S 6 and the N = 2 truncation obtained when S 6 is equipped with its nearly-Kähler structure, overlap in the N = 1, G 2 -invariant sector of the former.

Generalised Scherk-Schwarz reductions from gauged supergravity

“…A Coset representative decomposition 32 1 Introduction and summary There has been much recent activity in the study and construction of new consistent Kaluza-Klein truncations of supergravity theories [1][2][3][4][5][6][7]. Such truncations allow to identify a subsector of the configuration space of a theory compactified on an internal manifold, such that the dynamics are encoded in a lower-dimensional gauged supergravity and any solutions of the latter lift to solutions of its higher-dimensional parent.…”

“…These formalisms allow to repackage the field content of a supergravity theory in order to give a geometrical interpretation to their gauge symmetries and dualities. The long-sought proof of consistency of the truncation of type IIB supergravity on S 5 to SO (6) gauged maximal supergravity in five dimensions relied on the ExFT framework [2], and consistent truncations on spheres, hyperboloids, twisted tori and products thereof are now well-understood [2,7]. Results concerning sphere reductions of massive IIA supergravity [4][5][6] have also been rephrased in terms of ExFT and EGG [40,41].…”

“…These are ω-deformed SO(p, q), CSO(p, q, r), and 'dyonic CSO' gaugings. All these gaugings have been uplifted [2,[4][5][6][7] except for the ω-deformed SO(p, q) models, for which however the no-go result 2 See [22] for extra recent results on the S 7 truncation, [23] for a similar rewriting of type IIB supergravity, [3] for hyperboloid reductions based on the same techniques, and [4,6] for type IIA supergravity on a six-sphere. Also see [24][25][26] for other sphere reductions.…”

$$ \mathcal{N} $$ = 2 supersymmetric S-folds

“…Unlike for the SO(8) theory, much more is by now known about the dyonically-gauged ISO (7) supergravity that arises from the reduction of massive IIA supergravity on a sixsphere S 6 [15]. In this case the electromagnetic deformation parameter is a discrete (on/off) deformation, namely, it can be set to c = 0 or 1 without loss of generality [16].…”

Hypermultiplet gaugings and supersymmetric solutions from 11D and massive IIA supergravity on $$\hbox {H}^{(p,q)}$$ H ( p , q ) spaces

“…This symmetry is holographically identified with the R-symmetry of the dual field theory. In the ISO (7) case, this solution was presented in [10,24] 3 and uplifted to a background of massive IIA supergravity in [10,22]. The dual threedimensional SCFT was also identified in [10] as a super Chern-Simons-matter theory with simple gauge group SU(N ) and level k given by the Romans mass parameter.…”