## 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 programme 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 with an M-theory lift of closed strings described by an asymmetric cyclic orbifold of the (Formula presented.) 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.

Original language | English |
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Pages (from-to) | 1-42 |

Number of pages | 42 |

Journal | Letters in Mathematical Physics |

Early online date | 23 May 2017 |

DOIs | |

Publication status | E-pub ahead of print - 23 May 2017 |

## Keywords

- Bundle gerbes
- Fluxes in string and M-theory
- Higher geometric quantisation
- Higher geometric structures

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics