Quantum Wilson surfaces and topological interactions

Abstract

We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal $G$-bundle $P\to \Sigma$. Interestingly, it can interact topologically with 2-dimensional Yang-Mills and BF theories modifying their partition functions. We compute explicitly the partition function of the 2-dimensional Yang-Mills theory with a Wilson surface. The Wilson surface turns out to be nontrivial for the gauge group $G$ non-simply connected (and trivial for $G$ simply connected). In particular we study in detail the cases $G=SU(N)/{\mathbb{Z}}_m$, $G=Spin(4l)/({\mathbb{Z}}_2\oplus {\mathbb{Z}}_2)$ and obtain a general formula for any compact connected Lie group.

15 pages

References in corpus (3)

• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• M5-branes and Wilson Surfaces
• Wilson surface observables from equivariant cohomology

Cited by in corpus (3)

• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model