Fluxes, bundle gerbes and 2-Hilbert spaces

Abstract

We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a program of higher geometric quantisation of closed strings in flux compactifications and of M5-branes in C-fields. We review in detail the construction of the 2-category of bundle gerbes, and introduce the higher geometrical structures necessary to turn their categories of sections into 2-Hilbert spaces. We work out several explicit examples of 2-Hilbert spaces in the context of closed strings and M5-branes on flat space. We also work out the prequantum 2-Hilbert space associated to an M-theory lift of closed strings described by an asymmetric cyclic orbifold of the SU(2) WZW model, providing an example of sections of a torsion gerbe on a curved background. We describe the dimensional reduction of M-theory to string theory in these settings as a map from 2-isomorphism classes of sections of bundle gerbes to sections of corresponding line bundles, which is compatible with the respective monoidal structures and module actions.

38 pages; v2: Exposition improved, references added; Final version published in Letters in Mathematical Physics

References in corpus (7)

• T-duality and closed string non-commutative (doubled) geometry
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• More Morphisms between Bundle Gerbes
• Higher Symplectic Geometry
• Constructions with bundle gerbes
• 2-categorical Poincare Representations and State Sum Applications
• Twisted bundles and twisted K-theory

Cited by in corpus (10)

• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Geometry and 2-Hilbert Space for Nonassociative Magnetic Translations
• Magnetic monopoles and nonassociative deformations of quantum theory
• Smooth Functorial Field Theories from B-Fields and D-Branes
• Quantization of Magnetic Poisson Structures
• Principal $\infty$-Bundles and Smooth String Group Models
• Twisted loop transgression and higher Jandl gerbes over finite groupoids
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory
• Gerbes in Geometry, Field Theory, and Quantisation