## Abstract

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov-Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

Original language | English |
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Article number | 2150031 |

Journal | Reviews in Mathematical Physics |

Volume | 33 |

Issue number | 9 |

Early online date | 18 Jun 2021 |

DOIs | |

Publication status | Published - Oct 2021 |

## Keywords

- Born geometry
- doubled sigma-models
- Lie algebroid gauging
- Riemannian foliations
- T-duality

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics