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• W2808070027 abstract "It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing $${eta}$$ and an O(2d) generalized metric $${mathcal{H}}$$. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing $${omega}$$. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure $${(eta,omega,mathcal{H})}$$ and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics." @default.
• W2808070027 created "2018-06-21" @default.
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• W2808070027 date "2019-03-08" @default.
• W2808070027 modified "2023-10-06" @default.
• W2808070027 title "A Unique Connection for Born Geometry" @default.
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• W2808070027 doi "https://doi.org/10.1007/s00220-019-03379-7" @default.
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