Born sigma-models for para-Hermitian manifolds and generalized T-duality

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