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 → 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.

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Correspondence to Olga Chekeres.

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ArXiv ePrint: 1805.10992

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Chekeres, O. Quantum Wilson surfaces and topological interactions. J. High Energ. Phys. 2019, 30 (2019). https://doi.org/10.1007/JHEP02(2019)030

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Keywords

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