Gauged supergravity from the Lunin-Maldacena background

Abstract

We show how to expand the Lunin-Maldacena solution to the full bosonic sector of gauged N = 2 supergravity. In particular, we construct a consistent truncation of IIB supergravity on a βdeformed AdS 5 × S 5 background retaining a dynamical metric and graviphoton in five dimensions.We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution.

Systematics of consistent truncations from generalised geometry

“…At the technical level, this is shown by exploiting the fact that the TsT transformation has a simple action in generalised geometry via a bi-vector field. It was recently shown in the S 5 case that such backgrounds admitted a truncation to minimal gauged supergravity (8 supercharges) [23]. Our result shows that they in fact admit a much larger truncation to half-maximal supergravity with two vector multiplets.…”

“…A class of such backgrounds is provided by the β-deformation of Lunin and Maldacena [22]. For the case where the internal manifold is S 5 , the explicit truncation ansatz of type IIB supergravity on the β-deformed geometry to pure gauged supergravity has been given very recently in [23]. Here we show that if one starts from a toric Sasaki-Einstein manifold, the generalised SU (2) structure of the β-deformed background allows for a much larger truncation.…”

“…16 A minor subtlety is that the truncation of [20] was derived in the Einstein frame of type IIB supergravity, while the generalised metric in (A. 23) is adapted to the string frame; however (A.23) can be turned to the Einstein frame by simply ignoring the explicit factors of e −φ appearing there, and we do so in our computation. 17 In this case ∆ is not really a warp factor as it is independent of the internal coordinates.…”

Minimal D = 4 $$ \mathcal{N} $$ = 2 supergravity from D = 11: an M-theory free lunch

“…Thus, our results show that any (bosonic) solution of D = 4 N = 2 minimal gauged supergravity can be consistently uplifted to D = 11 on the seven-dimensional class of geometries of [12], and that the resulting D = 11 configuration will preserve any supersymmetries, up to N = 2, that the D = 4 configuration might have. Other consistent truncations to pure gauged supergravities in various dimensions on different G-structure geometries have been constructed in [13][14][15][16][17][18][19][20][21][22].…”

Minimal D 4 truncations of type I lA

“…Consistency is then shown by enforcing the higher-dimensional equations of motion on the lower-dimensional ones while making use of the torsion classes. This technique or variations thereof has been fruitfully applied in various contexts [24,25,[29][30][31][32][33][34][35][36][37][38][39][40]. G-structure analyses exist [41][42][43] for the N = 2 AdS 4 type IIA solution of [21] and generalisations thereof.…”