Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality

TL;DR

This paper develops a covariant framework for doubled sigma-models using para-Hermitian geometry, introducing generalized metrics and Born geometry to understand T-duality and non-geometric backgrounds in string theory.

Contribution

It provides a new geometric formulation of duality-symmetric string theory with para-Hermitian structures, linking Born geometry to sigma-models and generalized T-duality.

Findings

Defines generalized metrics on para-Hermitian manifolds.

Relates Born geometry to worldsheet sigma-models.

Describes geometric T-duality including non-abelian cases.

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.