Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulators

Abstract

The Feynman amplitudes with the two-dimensional Wess-Zumino action functional have a geometric interpretation as bundle gerbe holonomy. We present details of the construction of a distinguished square root of such holonomy and of a related 3d-index and briefly recall the application of those to the building of topological invariants for time-reversal-symmetric two- and three-dimensional crystals, both static and periodically forced.

26 pages, 9 figures

References in corpus (5)

• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological index for periodically driven time-reversal invariant 2D systems
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
• The basic bundle gerbe on unitary groups
• Global gauge anomalies in two-dimensional bosonic sigma models

Cited by in corpus (7)

• Tensor Berry connections and their topological invariants
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• 'Real' gerbes and Dirac cones of topological insulators
• The Fermi gerbe of Weyl semimetals
• Eigenvalue crossings in Floquet topological systems
• Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory