Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models

Abstract

We investigate doubled (generalized) complex structures in $2D$-dimensional Born geometries where T-duality symmetry is manifestly realized. We show that Kähler, hyperkähler, bi-hermitian and bi-hypercomplex structures of spacetime are implemented in Born geometries as doubled structures. We find that the Born structures and the generalized Kähler (hyperkähler) structures appear as subalgebras of bi-quaternions and split-tetra-quaternions. We find parts of these structures are classified by Clifford algebras. We then study the T-duality nature of the worldsheet instantons in Born sigma models. We show that the instantons in Kähler geometries are related to those in bi-hermitian geometries in a non-trivial way.

44 pages, minor corrections

References in corpus (7)

• Double Field Theory
• Doubled Geometry and T-Folds
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Non-geometric branes are DFT monopoles
• Generalised Kinematics for Double Field Theory
• Generalized Hyperkaehler Geometry and Supersymmetry
• Born sigma model for branes in exceptional geometry

Cited by in corpus (3)

• Yano F structures and extended Supersymmetry
• T-duality on Almost Hermitian Spaces
• Doubled space and extended supersymmetry