TQFT's and gerbes

Abstract

We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a one-to-one correspondence between their local description in terms of locally-defined functions and forms and their non-local description in terms of a suitable class of embedded TQFT's.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-14.abs.html

References in corpus (8)

• WZW branes and gerbes
• Higher Yang-Mills Theory
• Spin Foam Models of Matter Coupled to Gravity
• Differential Geometry of Gerbes
• Combinatorics of Non-Abelian Gerbes with Connection and Curvature
• Gerbes and homotopy quantum field theories
• A functorial approach to differential characters
• A classical approach to TQFT's

Cited by in corpus (8)

• Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory
• Abelian and non-Abelian branes in WZW models and gerbes
• The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
• Cohomological Twisting of 2-Linearization and Extended TQFT
• Super, quantum and non-commutative species
• Two-dimensional algebra in lattice gauge theory
• Homological Quantum Field Theory
• Gerbes in Geometry, Field Theory, and Quantisation