nLab coset WZW model

Idea

The generalization of the WZW model where target space is not necessarily a Lie group $G$, but a coset space $G/H$ for some subgroup $H$.

CS/WZW correspondence

There exists a well-known correspondence between 3d $G$-Chern-Simons theory, and the 2d $G$ Wess-Zumino-Witten model. It is then natural to ask what is the corresponding 3d theory to a 2d coset WZW model.

A first, fairly general, answer was proposed in (Moore & Seiberg 89), where it is claimed that for a $G/H$ coset model the corresponding 3d theory is $(G_k \times H_{-\tilde{k}})/Z$ Chern-Simons, with $k,\tilde{k}\geq 0$ some appropriate non-negative Chern-Simons levels, and $Z$ the common center. The role of the quotient by $Z$ is to remove additional copies of the vacuum not present in the coset model.

However, this general proposal fails in some specific coset models, now known as Maverick coset theories (see e.g. (Dunbar & Joshi 93)). These Maverick theories often arise when one of the groups is centerless. A more general proposal that is compatible with the known Maverick theories appears in (Cordova & Garcia-Sepulveda 23), where a Physics argument based on gauging a generalized global symmetry is provided.

Related concepts

• gauged WZW model

References

• Edward Witten, On holomorphic factorization of WZW and coset models, Comm. Math. Phys. Volume 144, Number 1 (1992), 189-212. (doi).

• Gregory Moore, and Nathan Seiberg. Taming the conformal zoo. Physics Letters B 220.3 (1989): 422-430.

• David Dunbar, and Keith Joshi. Maverick examples of coset conformal field theories. Modern Physics Letters A 8.29 (1993): 2803-2814. (doi).

• Clay Cordova, Diego García-Sepúlveda. Non-Invertible Anyon Condensation and Level-Rank Dualities (2023). (arXiv:2312.16317).