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

Vincenzo Emilio Marotta, Richard J. Szabo

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number2150031
JournalReviews in Mathematical Physics
Volume33
Issue number9
Early online date18 Jun 2021
DOIs
Publication statusPublished - 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

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