Workshop on Higher Gauge Theory

Where to look for higher gauge phenomena in nature (and in abstraction)?

Workshop description:

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.
These 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?

here

List of participants

Provisional schedule

Local Organising committee:

João Faria Martins (University of Leeds) main contact
Paul Martin (University of Leeds)
Fiona Torzewska (University of Leeds)

Venue: University of Leeds (campus map)

To register to attend please contact João (J.fariamartins @ leeds.ac.uk).
We gratefully acknowledge funding from Leeds University School of Mathematics, and (PM) from EPSRC.
Poster here when ready.

PM would like to thank Zoltan Kadar and Alison Parker
for valuable suggestions and help.

Links to useful resources

Anyonic loops moving in 3D space

Ice patterns at Ilkey Moor

Anyons moving in 2D space