Double Field Theory and Pseudo-Supersymmetry

TL;DR

This paper reformulates ${ m O}(D) imes{ m O}(D)$ covariant pseudo-supersymmetric extensions of the bosonic string in arbitrary dimensions using generalised geometry, exploring solutions like Minkowski$ imes G$ vacua and squashed group manifolds.

Contribution

It recasts pseudo-supersymmetric string actions in the language of generalised geometry with explicit covariant derivatives and analyzes specific vacuum solutions.

Findings

Constructed ${ m O}(D) imes{ m O}(D)$ covariant actions and supersymmetry rules.

Identified Minkowski$ imes G$ vacuum solutions with pseudo-supersymmetry.

Explored solutions on squashed group manifolds, including Lorentzian signatures.

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 $G$.