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Journal of High Energy Physics

, 2019:30 | Cite as

Quantum Wilson surfaces and topological interactions

  • Olga ChekeresEmail author
Open Access
Regular Article - Theoretical Physics
  • 12 Downloads

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.

Keywords

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

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GenevaGenève 4Switzerland

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