AdS4 solutions of massive IIA from dyonic ISO(7) supergravity

Abstract

Explicit formulae are given for the consistent truncation of massive type IIA supergravity on the six-sphere to the SU(3)-invariant sector of D = 4 N = 8 supergravity with dyonic ISO(7) gauging. These formulae are then used to construct AdS 4 solutions of massive type IIA via uplift on S 6 of the critical points of the D = 4 supergravity with at least SU(3) symmetry. We find a new N = 1 solution with SU(3) symmetry, a new non-supersymmetric solution with SO(6) symmetry, and recover previously known solutions. We quantise the fluxes, calculate the gravitational free energies of the solutions and discuss the stability of the non-supersymmetric ones. Among these, a (previously known) G 2 -invariant solution is found to be stable. factor, these solutions are typically supported by internal values of the supergravity forms. The metrics on the internal S 7 and S 5 are usually inhomogeneous and display isometry groups smaller than SO(8) and SO(6). A two-step variant of this uplifting method was introduced in [20], where a spherical truncation to some intermediate dimension, e.g. D = 7 [21, 22], followed by a further reduction on a suitable (usually hyperbolic) space was performed to obtain supersymmetric AdS 4 or AdS 5 solutions.All of the above AdS 4 and AdS 5 direct product solutions and most (but not all, see e.g.[23]) of the warped products are partially supported by a non-vanishing ('electric') Freund-Rubin-like termF (4) ∼ vol(AdS) 4 in D = 11 andF (5) ∼ vol(AdS) 5 in type IIB. This reflects that the corresponding solutions describe conformal phases of the M2, D3 and, for [23], M5 brane field theories. Since type IIA supergravity also contains a four-form field strengthF 4 , it would be natural to expect that the above plethora of AdS 4 solutions in D = 11 had a counterpart in type IIA. However, this is not the case: excluding the massless IIA solutions obtained by circle reduction from D = 11, only a handful of AdS 4 solutions in type IIA are known, either smooth and sourcelss or singular and with sources. And most of them are only known numerically.Massive type IIA supergravity [24] does admit a direct product Freund-Rubin solution AdS 4 ×S 6 [24], where S 6 is equipped with the usual, round, homogeneous, SO(7)-symmetric metric: see equation (4.8). However, unlike its maximally supersymmetric counterparts in D = 11 [4] and type IIB [5], it breaks all supersymmetries. Furthermore, as it will be argued below, this solution is unstable. G-structure methods have been used to classify supersymmetric AdS 4 solutions in type IIA (as well as in other contexts) and, in some cases, these results have led to explicit classes of solutions. N = 1 AdS 4 solutions with SU(3)-structure were classified in [25] and [26]. An explicit class of N = 1 solutions of massive type IIA involving the direct product of AdS 4 with a nearly-Kähler six-dimensional manifold was discovered in [25]. This class includes, in particular, the homogeneous N = 1 direct product AdS 4 × S 6 , where the six-sphere is now regarded as S 6 = G 2 /SU(3) and ...

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

“…See section 5 for further comments on the g = 0 case. Finally, we have fixed the coefficients in (3.3)-(3.7) by solving the field equations in various invariant sectors, including the G 2 (see section 4.1) and SU(3) [51] sectors, and then imposing the IIA equations of motion. In particular, the SU(3) × U(1)-invariant N = 2 AdS 4 solution of [19] fixes some of these coefficients.…”

Universal properties of Kaluza-Klein gravitons

“…In order to narrow down and simplify the problem, we will further focus on the SU(3)-invariant sector of these gaugings. This sector has been explicitly uplifted to the respective higher-dimensional supergravities [18,19,20], and the corresponding vacua have been charted [21,10,20]. The list of AdS vacua in this sector across all three gaugings of interest has been summarised for convenience in table 1.…”

Observables in the Guarino-Jafferis-Varela/CS-SYM duality

“…In the GJV solution there is no such phase transition [17], since the coupling g α s remains bounded,…”

“…Solutions with this symmetry also admit dyonic gaugings [10], studied further in [14], and it has been proved [15] that the purely electric solutions can be embedded into D = 11 supergravity as a consistent truncation on S 6 × S 1 . Moreover, the dyonic ISO(7) gauged SUGRA solutions arise as consistent truncations of massive type IIA solution on a squashed 6-sphere (shown also in [16]), that we denote by SS 5 , and preserve up to N = 3 supersymmetries [3,[17][18][19] of the total N = 8. The magnetic coupling constant m is identified with the Romans mass F 0 .…”