Quantum Wilson surfaces and topological interactions

Abstract

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 → Σ. Interestingly, it can interact topologically with 2-dimensional Yang-Mills and BF theories modifying their partition functions. This gives a new interpretation of the results obtained in [1]. We compute explicitly the partition function of the 2-dimensional Yang-Mills theory interacting with a Wilson surface for the cases G = SU(N)/ℤ m , G = Spin(4l)/(ℤ2 ⊕ ℤ2) and obtain a general formula for any compact connected Lie group.