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Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality | | Vincenzo Emilio Marotta
; Richard J. Szabo
; | | Date: |
22 Oct 2019 | | 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. | | Source: | arXiv, 1910.9997 | | Services: | Forum | Review | PDF | Favorites | |
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