Abstract
We present a generalised geometry framework for systematically constructing consistent truncations of ten- and eleven-dimensional supergravity preserving varying fractions of supersymmetry. Truncations arise when there is a reduced structure group GS of the exceptional generalised geometry, such that the intrinsic torsion is a GS -singlet. The matter content of the truncated theory follows from group-theoretical arguments, while the gauging is determined by the sub-algebra of generalised diffeomorphisms generated by the GS -singlet vectors. After discussing the general ideas across different spacetime dimensions and amounts of supersymmetry, we provide detailed formulae for truncations to gauged half-maximal supergravity in five dimensions. In particular, we establish an expression for the generalised metric on the exceptional tangent bundle, which determines the scalar truncation ansatz. As applications, we show that this formalism gives a simple derivation of a new consistent truncation of type IIB supergravity on β-deformed Lunin-Maldacena geometries, yielding half-maximal supergravity coupled to two vector multiplets, and of the truncation of eleven-dimensional supergravity on Maldacena-Núñez geometries, given by S4 twisted over a Riemann surface, which leads to half-maximal supergravity coupled to three vector multiplets.
Highlights
A common problem in string theory and supergravity is how to derive lower-dimensional effective theories
We present a generalised geometry framework for systematically constructing consistent truncations of ten- and eleven-dimensional supergravity preserving varying fractions of supersymmetry
We establish an expression for the generalised metric on the exceptional tangent bundle, which determines the scalar truncation ansatz. We show that this formalism gives a simple derivation of a new consistent truncation of type IIB supergravity on β-deformed Lunin-Maldacena geometries, yielding half-maximal supergravity coupled to two vector multiplets, and of the truncation of eleven-dimensional supergravity on Maldacena-Nunez geometries, given by S4 twisted over a Riemann surface, which leads to half-maximal supergravity coupled to three vector multiplets
Summary
A common problem in string theory and supergravity is how to derive lower-dimensional effective theories. The key requirement is that the so-called “intrinsic torsion” [18] of the G-structure contains only singlets This formalism allows one to determine all the features of the lower-dimensional gauged supergravity, such as the amount of supersymmetry, the coset manifold of the scalars, the number of gauge and tensor fields, and the gauging, all directly from the geometry. We first illustrate how the formalism works by reproducing the truncation of type IIB supergravity on squashed Sasaki-Einstein manifolds derived in [20, 21] This is half-maximal supergravity coupled to two vector multiplets and with a U(1)×Heis gauging, where Heis denotes the Heisenberg group.
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