nLab 4d WZW model

Idea

The 4-dimensional version of higher dimensional WZW theory, the boundary theory of the 5-dimensional Chern-Simons theory that is induced from the third Chern class. Also called Nair-Schiff theory or Kähler Chern-Simons theory .

Properties

Equations of motion

The Euler-Lagrange equations of the 4d WZW model are those of self-dual Yang-Mills theory.

Finiteness

The model is finite at 1-loop (Ketov) and expected to be finite to all orders.

References

• Ali Chamseddine, Phys. Lett. B233, 291 (1989);

• V.P.Nair, Kähler-Chern-Simons Theory (arXiv:hep-th/9110042)

• A. Losev, Greg Moore, Nikita Nekrasov, Samson Shatashvili, Four-Dimensional Avatars of Two-Dimensional RCFT (arXiv:hep-th/9509151)

• Takeo Inami, Hiroaki Kanno, Tatsuya Ueno, Chuan-Sheng Xiong, Two-toroidal Lie Algebra as Current Algebra of Four-dimensional Kähler WZW Model (arXiv:hep-th/9610187)

• A. V. Ketov, Phys.Lett. B383 (1996) 390-396

• T. Inami, H. Kanno and T. Ueno, Mod. Phys. Lett. A12, 2757 (1997).

• J. Gegenberg , G. Kunstatter, Boundary Dynamics of Higher Dimensional AdS Spacetime (arXiv:hep-th/9905228)

• J. Gegenberg , G. Kunstatter, Boundary Dynamics of Higher Dimensional Chern-Simons Gravity (arXiv:hep-th/0010020)