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Understanding WZW Theories with Chern-Simons Theories and Vice-Versa
| Content Provider | Semantic Scholar |
|---|---|
| Author | Cormack, Ian Mac |
| Copyright Year | 2018 |
| Abstract | We examine the correspondence between 2+1 dimensional pure Chern-Simons gauge theories with a semi simple, compact gauge group and 1+1 dimensional Wess-ZuminoWitten (WZW) conformal field theories. We first introduce WZW models as conformal field theories with an additional symmetry group described by an algebra of current operators. The operator product expansions and the stress tensor of the theory are calculated and compared to those of a conventional CFT. We then introduce the classical Chern-Simons action, quantize it by imposing the Gauss law constraint, and show that the physical wave functionals satisfying the constraint correspond exactly to the path integral of the WZW action with the Chern-Simons gauge field A as a source. This correspondence is the core of the relationship between CS and WZW theories. We go on to compute WZW current correlators as well as Chern-Simons Wilson lines. The latter are shown to correspond to primary field insertions in the WZW generating functional. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://theory.uchicago.edu/~sethi/Teaching/P483-W2018/WZW_paper_imaccormack.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
