A Unique Connection for Born Geometry

Freidel, Laurent; Rudolph, Felix J. und Svoboda, David (2019): A Unique Connection for Born Geometry. In: Communications in Mathematical Physics, Bd. 372, Nr. 1: S. 119-150

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 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, 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 0010-3616
• Sprache: Englisch