Higher gauge theory is a generalisation of ordinary gauge theory with additional levels of structure and of symmetry.
A key feature of higher gauge theory is parallel transport along surfaces.
Higher gauge theory is mathematically coherent and natural, but a role for higher gauge models in physics has yet to be confirmed.
Mechanisms whereby higher gauge systems could appear in nature
have recently been discovered.
include via M-theory, quantum gravity, and topological phases of matter with emergent higher gauge symmetry.
These are some of the questions we want to discuss:
Where would we expect physics modelled by higher gauge symmetry to appear?
Does higher gauge symmetry have any role for modelling emergent phenomena.
And which type of emergent string quasi-particles are expected?
What type of higher order representation theory
(e.g. categorical representations of 2-groups)
is relevant for modelling higher gauge particles and strings?
Are there possible applications to topological quantum computing
(e.g. through moving loop particles on 3+1D topological phases)?
Are there applications to 4-dimensional geometric topology;
e.g. invariants of loop braids, knotted surfaces, and of 4D manifolds?