Abstract
Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting pseudo-supersymmetric theories can be defined in arbitrary spacetime dimensions. We focus here on the ${\cal N}=1$ pseudo-supersymmetric extensions of the arbitrary-dimensional bosonic string action, which were constructed a few years ago. In this paper, we recast these in the language of generalised geometry. More precisely, we construct the action and the corresponding supersymmetry transformation rules in terms of O($D$)$\times$O($D$) covariant derivatives, and we discuss consistent truncations on manifolds with generalised $G$-structure. As explicit examples, we discuss Minkowski$\times G$ vacuum solutions and their corresponding pseudo-supersymmetry. We also briefly discuss squashed group manifold solutions, including an example with a Lorentzian signature metric on the group manifold $G$.
Highlights
Supersymmetry provides a powerful tool for probing aspects of physics that would otherwise be beyond the limits of computability
We focus here on the N 1⁄4 1 pseudo-supersymmetric extensions of the arbitrary-dimensional bosonic string action, which were constructed a few years ago
We record some relevant properties of spinors in general dimensions; we present some details of the calculations showing that the N 1⁄4 1 pseudo-supersymmetric string can be recast in a DFT framework; we give some useful representations for Dirac matrices in dimensionally reduced spacetimes; and we construct an example of a ðMinkowskiÞD−dim G × G background, for G 1⁄4 SOð5Þ, where the metric on the group is squashed
Summary
Supersymmetry provides a powerful tool for probing aspects of physics that would otherwise be beyond the limits of computability. A natural question in this context is whether pseudo-supersymmetry permits a similar treatment We answer this question in the affirmative and demonstrate that it is possible to extend the existing results of supersymmetric DFT from 10 dimensions to arbitrary dimensions. We record some relevant properties of spinors in general dimensions; we present some details of the calculations showing that the N 1⁄4 1 pseudo-supersymmetric string can be recast in a DFT framework; we give some useful representations for Dirac matrices in dimensionally reduced spacetimes; and we construct an example of a ðMinkowskiÞD−dim G × G background, for G 1⁄4 SOð5Þ, where the metric on the group is squashed.
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