Unitary Chern-Simons matrix model and the Villain lattice action

Mauricio Andrés Romo Jorquera Miguel Tierz

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2206.74008

We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds to the q->1 limit of the Chern-Simons theory while the strong-coupling regime is related to the q->0 limit. In the latter case, there is a logarithmic relationship between the respective coupling constants. We also show how the Chern-Simons matrix model arises by considering two-dimensional Yang-Mills theory with the Villain action. This leads to a U(1)^N theory which is the Abelianization of 2d Yang-Mills theory with the heat-kernel lattice action. In addition, we show that the character expansion of the Villain lattice action gives the q deformation of the heat kernel as it appears in q-deformed 2d Yang-Mills theory. We also study the relationship between the unitary and Hermitian Chern-Simons matrix models and the rotation of the integration contour in the corresponding integrals.
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  title={Unitary Chern-Simons matrix model and the Villain lattice action},
  author={Mauricio Andrés Romo Jorquera, and Miguel Tierz},
Mauricio Andrés Romo Jorquera, and Miguel Tierz. Unitary Chern-Simons matrix model and the Villain lattice action. 2012. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220606162743486431331.
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