Journal of High Energy Physics

, 2019:30 | Cite as

Quantum Wilson surfaces and topological interactions

  • Olga ChekeresEmail author
Open Access
Regular Article - Theoretical Physics


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)/m, G = Spin(4l)/(ℤ2 ⊕ ℤ2) and obtain a general formula for any compact connected Lie group.


Field Theories in Lower Dimensions Topological Field Theories Sigma Models Wilson, ’t Hooft and Polyakov loops 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GenevaGenève 4Switzerland

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